(a) We know that a number is divisible by 3 if the sum of all digits is divisible by 3. Therefore, Smallest digit : 2 → 26724 = 2 + 6 + 7 + 2 + 4 = 21 Largest digit : 8 → 86724 = 8 + 6 + 7 + 2 + 4 = 27 (b) We know that a number is divisible by 3 if the sum of all digits is divisible by 3. Therefore,Read more
(a) We know that a number is divisible by 3 if the sum of all digits is divisible by 3.
Therefore, Smallest digit : 2 → 26724 = 2 + 6 + 7 + 2 + 4 = 21
Largest digit : 8 → 86724 = 8 + 6 + 7 + 2 + 4 = 27
(b) We know that a number is divisible by 3 if the sum of all digits is divisible by 3.
Therefore, Smallest digit : 0 → 476502 = 4 + 7 + 6 + 5 + 0 + 2 = 24
Largest digit : 9 → 476592 = 4 + 7 + 6 + 5 + 0 + 2 = 33
(a) 5445 → Sum of the digits at odd places = 4 + 5 = 9 → Sum of the digits at even places = 4 + 5 = 9 → Difference of both sums = 9 – 9 = 0 Since the difference is 0, therefore, the number is divisible by 11. (b) 10824 → Sum of the digits at odd places = 4 + 8 +1 = 13 → Sum of the digits at even plaRead more
(a) 5445 → Sum of the digits at odd places = 4 + 5 = 9
→ Sum of the digits at even places = 4 + 5 = 9
→ Difference of both sums = 9 – 9 = 0
Since the difference is 0, therefore, the number is divisible by 11.
(b) 10824 → Sum of the digits at odd places = 4 + 8 +1 = 13
→ Sum of the digits at even places = 2 + 0 = 2
→ Difference of both sums = 13 – 2 = 11
Since the difference is 11, therefore, the number is divisible by 11.
(c) 7138965 → Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24
→ Sum of the digits at even places = 6 + 8 + 1 = 15
→ Difference of both sums = 24 – 15 = 9
Since the difference is neither 0 nor 11, therefore, the number is not divisible by 11.
(d) 70169308 → Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17
→ Sum of the digits at even places = 0 + 9 + 1 + 7 = 17
→ Difference of both sums = 17 – 17 = 0
Since the difference is 0, therefore, the number is divisible by 11.
(e) 10000001 → Sum of the digits at odd places = 1 + 0 + 0 + 0 = 1
→ Sum of the digits at even places = 0 + 0 + 0 + 1 = 1
→ Difference of both sums = 1 – 1 = 0
Since the difference is 0, therefore, the number is divisible by 11.
(f) 901153 → Sum of the digits at odd places = 3 + 1 + 0 = 4
→ Sum of the digits at even places = 5 + 1 + 9 = 15
→ Difference of both sums = 15 – 4 = 11
Since the difference is 11, therefore, the number is divisible by 11.
(a) 297144 → Divisible by 2 as its units place is an even number. → Divisible by 3 as sum of its digits (= 27) is divisible by 3. Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6. (b) 1258 → Divisible by 2 as its units place is an even number. → Not divisible by 3Read more
(a) 297144 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 27) is divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6.
(b) 1258 → Divisible by 2 as its units place is an even number.
→ Not divisible by 3 as sum of its digits (= 16) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(c) 4335 → Not divisible by 2 as its units place is not an even number.
→ Divisible by 3 as sum of its digits (= 15) is divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(d) 61233 → Not divisible by 2 as its units place is not an even number.
→ Divisible by 3 as sum of its digits (= 15) is divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(e) 901352 → Divisible by 2 as its units place is an even number.
→ Not divisible by 3 as sum of its digits (= 20) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(f) 438750 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 27) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.
(g) 1790184 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 30) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.
(h) 12583 → Not divisible by 2 as its units place is not an even number.
→ Not divisible by 3 as sum of its digits (= 19) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(i) 639210 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 21) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.
(j) 17852 → Divisible by 2 as its units place is an even number.
→ Not divisible by 3 as sum of its digits (= 23) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(a) 572 → Divisible by 4 as its last two digits are divisible by 4. → Not divisible by 8 as its last three digits are not divisible by 8. (b) 726352 → Divisible by 4 as its last two digits are divisible by 4. → Divisible by 8 as its last three digits are divisible by 8. (c) 5500 → Divisible by 4 asRead more
(a) 572 → Divisible by 4 as its last two digits are divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(b) 726352 → Divisible by 4 as its last two digits are divisible by 4.
→ Divisible by 8 as its last three digits are divisible by 8.
(c) 5500 → Divisible by 4 as its last two digits are divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(d) 6000 → Divisible by 4 as its last two digits are 0.
→ Divisible by 8 as its last three digits are 0.
(e) 12159 → Not divisible by 4 and 8 as it is an odd number.
(f) 14560 → Divisible by 4 as its last two digits are divisible by 4.
→ Divisible by 8 as its last three digits are divisible by 8.
(g) 21084 → Divisible by 4 as its last two digits are divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(h) 31795072 → Divisible by 4 as its last two digits are divisible by 4.
→ Divisible by 8 as its last three digits are divisible by 8.
(i) 1700 → Divisible by 4 as its last two digits are 0.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(j) 5500 → Not divisible by 4 as its last two digits are not divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(a) A number which has only two factors is called a Prime numbe. (b) A number which has more than two factors is called a Composite number. (c) 1 neither Prime number nor Composite number. (d) The smallest prime number is 2. (e) The smallest composite number is 4. (f) The smallest even number is 2.Read more
(a) A number which has only two factors is called a Prime numbe.
(b) A number which has more than two factors is called a Composite number.
(c) 1 neither Prime number nor Composite number.
(d) The smallest prime number is 2.
(e) The smallest composite number is 4.
(f) The smallest even number is 2.
Write the smallest digit and the largest digit in the blanks space of each of the following numbers so that the number formed is divisibly by 3: (a) __________ 6724 (b) 4765 __________ 2
(a) We know that a number is divisible by 3 if the sum of all digits is divisible by 3. Therefore, Smallest digit : 2 → 26724 = 2 + 6 + 7 + 2 + 4 = 21 Largest digit : 8 → 86724 = 8 + 6 + 7 + 2 + 4 = 27 (b) We know that a number is divisible by 3 if the sum of all digits is divisible by 3. Therefore,Read more
(a) We know that a number is divisible by 3 if the sum of all digits is divisible by 3.
Therefore, Smallest digit : 2 → 26724 = 2 + 6 + 7 + 2 + 4 = 21
Largest digit : 8 → 86724 = 8 + 6 + 7 + 2 + 4 = 27
(b) We know that a number is divisible by 3 if the sum of all digits is divisible by 3.
Therefore, Smallest digit : 0 → 476502 = 4 + 7 + 6 + 5 + 0 + 2 = 24
Largest digit : 9 → 476592 = 4 + 7 + 6 + 5 + 0 + 2 = 33
https://www.tiwariacademy.com/ncert-solutions/class-6/maths/chapter-3/
See lessUsing divisibility test, determine which of the following numbers are divisible by 11: (a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001 (f) 901153
(a) 5445 → Sum of the digits at odd places = 4 + 5 = 9 → Sum of the digits at even places = 4 + 5 = 9 → Difference of both sums = 9 – 9 = 0 Since the difference is 0, therefore, the number is divisible by 11. (b) 10824 → Sum of the digits at odd places = 4 + 8 +1 = 13 → Sum of the digits at even plaRead more
(a) 5445 → Sum of the digits at odd places = 4 + 5 = 9
→ Sum of the digits at even places = 4 + 5 = 9
→ Difference of both sums = 9 – 9 = 0
Since the difference is 0, therefore, the number is divisible by 11.
(b) 10824 → Sum of the digits at odd places = 4 + 8 +1 = 13
→ Sum of the digits at even places = 2 + 0 = 2
→ Difference of both sums = 13 – 2 = 11
Since the difference is 11, therefore, the number is divisible by 11.
(c) 7138965 → Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24
→ Sum of the digits at even places = 6 + 8 + 1 = 15
→ Difference of both sums = 24 – 15 = 9
Since the difference is neither 0 nor 11, therefore, the number is not divisible by 11.
(d) 70169308 → Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17
→ Sum of the digits at even places = 0 + 9 + 1 + 7 = 17
→ Difference of both sums = 17 – 17 = 0
Since the difference is 0, therefore, the number is divisible by 11.
(e) 10000001 → Sum of the digits at odd places = 1 + 0 + 0 + 0 = 1
→ Sum of the digits at even places = 0 + 0 + 0 + 1 = 1
→ Difference of both sums = 1 – 1 = 0
Since the difference is 0, therefore, the number is divisible by 11.
(f) 901153 → Sum of the digits at odd places = 3 + 1 + 0 = 4
→ Sum of the digits at even places = 5 + 1 + 9 = 15
→ Difference of both sums = 15 – 4 = 11
Since the difference is 11, therefore, the number is divisible by 11.
https://www.tiwariacademy.com/ncert-solutions/class-6/maths/chapter-3/
See lessUsing divisibility test, determine which of the following numbers are divisible by 6: (a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852
(a) 297144 → Divisible by 2 as its units place is an even number. → Divisible by 3 as sum of its digits (= 27) is divisible by 3. Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6. (b) 1258 → Divisible by 2 as its units place is an even number. → Not divisible by 3Read more
(a) 297144 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 27) is divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6.
(b) 1258 → Divisible by 2 as its units place is an even number.
→ Not divisible by 3 as sum of its digits (= 16) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(c) 4335 → Not divisible by 2 as its units place is not an even number.
→ Divisible by 3 as sum of its digits (= 15) is divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(d) 61233 → Not divisible by 2 as its units place is not an even number.
→ Divisible by 3 as sum of its digits (= 15) is divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(e) 901352 → Divisible by 2 as its units place is an even number.
→ Not divisible by 3 as sum of its digits (= 20) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(f) 438750 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 27) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.
(g) 1790184 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 30) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.
(h) 12583 → Not divisible by 2 as its units place is not an even number.
→ Not divisible by 3 as sum of its digits (= 19) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
(i) 639210 → Divisible by 2 as its units place is an even number.
→ Divisible by 3 as sum of its digits (= 21) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.
(j) 17852 → Divisible by 2 as its units place is an even number.
→ Not divisible by 3 as sum of its digits (= 23) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.
https://www.tiwariacademy.com/ncert-solutions/class-6/maths/chapter-3/
See lessUsing divisibility test, determine which of the following numbers are divisibly by 4; by 8: (a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159 (f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150
(a) 572 → Divisible by 4 as its last two digits are divisible by 4. → Not divisible by 8 as its last three digits are not divisible by 8. (b) 726352 → Divisible by 4 as its last two digits are divisible by 4. → Divisible by 8 as its last three digits are divisible by 8. (c) 5500 → Divisible by 4 asRead more
(a) 572 → Divisible by 4 as its last two digits are divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(b) 726352 → Divisible by 4 as its last two digits are divisible by 4.
→ Divisible by 8 as its last three digits are divisible by 8.
(c) 5500 → Divisible by 4 as its last two digits are divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(d) 6000 → Divisible by 4 as its last two digits are 0.
→ Divisible by 8 as its last three digits are 0.
(e) 12159 → Not divisible by 4 and 8 as it is an odd number.
(f) 14560 → Divisible by 4 as its last two digits are divisible by 4.
→ Divisible by 8 as its last three digits are divisible by 8.
(g) 21084 → Divisible by 4 as its last two digits are divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(h) 31795072 → Divisible by 4 as its last two digits are divisible by 4.
→ Divisible by 8 as its last three digits are divisible by 8.
(i) 1700 → Divisible by 4 as its last two digits are 0.
→ Not divisible by 8 as its last three digits are not divisible by 8.
(j) 5500 → Not divisible by 4 as its last two digits are not divisible by 4.
→ Not divisible by 8 as its last three digits are not divisible by 8.
https://www.tiwariacademy.com/ncert-solutions/class-6/maths/chapter-3/
See lessFill in the blanks: (a) A number which has only two factors is called a _______________. (b) A number which has more than two factors is called a _______________. (c) 1 neither _______________ nor _______________. (d) The smallest prime number is _______________. (e) The smallest composite number is _______________. (f) The smallest even number is _______________.
(a) A number which has only two factors is called a Prime numbe. (b) A number which has more than two factors is called a Composite number. (c) 1 neither Prime number nor Composite number. (d) The smallest prime number is 2. (e) The smallest composite number is 4. (f) The smallest even number is 2.Read more
(a) A number which has only two factors is called a Prime numbe.
(b) A number which has more than two factors is called a Composite number.
(c) 1 neither Prime number nor Composite number.
(d) The smallest prime number is 2.
(e) The smallest composite number is 4.
(f) The smallest even number is 2.
https://www.tiwariacademy.com/ncert-solutions/class-6/maths/chapter-3/
See less