The Food Products Order (FPO) is a government order issued in India that regulates the manufacture, storage, distribution, sale, and import of food products. The FPO sets standards for the quality, safety, and labeling of food product and requires that food products meet these standards in order toRead more
The Food Products Order (FPO) is a government order issued in India that regulates the manufacture, storage, distribution, sale, and import of food products. The FPO sets standards for the quality, safety, and labeling of food product and requires that food products meet these standards in order to be sold in India. The order also establishes penalties for violating these standards and for engaging in any deceptive or fraudulent practices.
867 and 255 Since 867 > 255, we apply the division lemma to 867 and 255 to obtain 867 = 255 × 3 + 102 Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain 255 = 102 × 2 + 51 We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain 102 =Read more
867 and 255
Since 867 > 255, we apply the division lemma to 867 and 255 to obtain
867 = 255 × 3 + 102
Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain
255 = 102 × 2 + 51
We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain
102 = 51 × 2 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 51, Therefore, HCF of 867 and 255 is 51.
Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r for some integer q ≥ 0 and r = 0, 1, 2, 3, 4, 5 because 0 ≤ r < 6. Therefore, a = 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4 or 6q + 5 Also, 6q + 1 = 2 × 3q + 1 = 2k1 + 1, where k1 is a positive integer 6q + 3 = (6qRead more
Let a be any positive integer and b = 6.
Then, by Euclid’s algorithm, a = 6q + r for some integer q ≥ 0 and r = 0, 1, 2, 3, 4, 5 because 0 ≤ r < 6.
Therefore, a = 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4 or 6q + 5 Also,
6q + 1 = 2 × 3q + 1 = 2k1 + 1, where k1 is a positive integer
6q + 3 = (6q + 2) + 1 = 2 (3q + 1) + 1 = 2k₂ + 1, where k₂ is an integer
6q + 5 = (6q + 4) + 1 = 2 (3q + 2) + 1 = 2k₃ + 1, where k₃ is an integer
Clearly, 6q + 1, 6q + 3, 6q + 5 are of the form 2k + 1, where k is an integer.
Therefore, 6q + 1, 6q + 3, 6q + 5 are not exactly divisible by 2.
Hence, these expressions of numbers are odd numbers and therefore, any odd integer can be expressed in the form 6q + 1, or 6q + 3, or 6q + 5.
You will be happy to know that there is a Video Solution for this question as well. See here 🧐
This is a very simple question 😃 Answer, HCF (616, 32) will give the maximum number of columns in which they can march. We can use Euclid’s algorithm to find the HCF. 616 = 32 × 19 + 8 32 = 8 × 4 + 0 The HCF (616, 32) is 8. Therefore, they can march in 8 columns each. See this for complete ExplanatiRead more
This is a very simple question 😃
Answer,
HCF (616, 32) will give the maximum number of columns in which they can march.
We can use Euclid’s algorithm to find the HCF.
616 = 32 × 19 + 8
32 = 8 × 4 + 0
The HCF (616, 32) is 8. Therefore, they can march in 8 columns each.
Find the LCM and HCF of the following integers by applying the prime factorization method. 8, 9 and 25
8, 9 and 25 8 = 2 × 2 × 2 = 2³ 9 = 3 × 3 = 3² 25 = 5 × 5 = 5² HCF = 1 LCM = 2³ × 3² × 5² = 8 × 9 × 25 = 1800 See this 👇
8, 9 and 25
8 = 2 × 2 × 2 = 2³
9 = 3 × 3 = 3²
25 = 5 × 5 = 5²
HCF = 1
LCM = 2³ × 3² × 5² = 8 × 9 × 25 = 1800
See this 👇
See lessThe agency which provides certificates of reliability to food products is
The Food Products Order (FPO) is a government order issued in India that regulates the manufacture, storage, distribution, sale, and import of food products. The FPO sets standards for the quality, safety, and labeling of food product and requires that food products meet these standards in order toRead more
The Food Products Order (FPO) is a government order issued in India that regulates the manufacture, storage, distribution, sale, and import of food products. The FPO sets standards for the quality, safety, and labeling of food product and requires that food products meet these standards in order to be sold in India. The order also establishes penalties for violating these standards and for engaging in any deceptive or fraudulent practices.
See lessUse Euclid’s division algorithm to find the HCF of : 867 and 255
867 and 255 Since 867 > 255, we apply the division lemma to 867 and 255 to obtain 867 = 255 × 3 + 102 Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain 255 = 102 × 2 + 51 We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain 102 =Read more
867 and 255
Since 867 > 255, we apply the division lemma to 867 and 255 to obtain
867 = 255 × 3 + 102
Since remainder 102 ≠ 0, we apply the division lemma to 255 and 102 to obtain
255 = 102 × 2 + 51
We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain
102 = 51 × 2 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 51, Therefore, HCF of 867 and 255 is 51.
Here is the Video Solution see here 👀
See lessShow that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r for some integer q ≥ 0 and r = 0, 1, 2, 3, 4, 5 because 0 ≤ r < 6. Therefore, a = 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4 or 6q + 5 Also, 6q + 1 = 2 × 3q + 1 = 2k1 + 1, where k1 is a positive integer 6q + 3 = (6qRead more
Let a be any positive integer and b = 6.
Then, by Euclid’s algorithm, a = 6q + r for some integer q ≥ 0 and r = 0, 1, 2, 3, 4, 5 because 0 ≤ r < 6.
Therefore, a = 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4 or 6q + 5 Also,
6q + 1 = 2 × 3q + 1 = 2k1 + 1, where k1 is a positive integer
6q + 3 = (6q + 2) + 1 = 2 (3q + 1) + 1 = 2k₂ + 1, where k₂ is an integer
6q + 5 = (6q + 4) + 1 = 2 (3q + 2) + 1 = 2k₃ + 1, where k₃ is an integer
Clearly, 6q + 1, 6q + 3, 6q + 5 are of the form 2k + 1, where k is an integer.
Therefore, 6q + 1, 6q + 3, 6q + 5 are not exactly divisible by 2.
Hence, these expressions of numbers are odd numbers and therefore, any odd integer can be expressed in the form 6q + 1, or 6q + 3, or 6q + 5.
You will be happy to know that there is a Video Solution for this question as well. See here 🧐
See lessAn army contingent of 616 members is to march behind an army band of 32 member’s in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
This is a very simple question 😃 Answer, HCF (616, 32) will give the maximum number of columns in which they can march. We can use Euclid’s algorithm to find the HCF. 616 = 32 × 19 + 8 32 = 8 × 4 + 0 The HCF (616, 32) is 8. Therefore, they can march in 8 columns each. See this for complete ExplanatiRead more
This is a very simple question 😃
Answer,
HCF (616, 32) will give the maximum number of columns in which they can march.
We can use Euclid’s algorithm to find the HCF.
616 = 32 × 19 + 8
32 = 8 × 4 + 0
The HCF (616, 32) is 8. Therefore, they can march in 8 columns each.
See this for complete Explanation 😃😄
See less