NCERT Solutions for Class 10 Maths Chapter 1
Important NCERT Questions
Real Numbers
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 1.2
Page No:11
Questions No:5
Check whether 6ⁿ can end with the digit 0 for any natural number n.
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If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5.
Prime factorisation of 6ⁿ = (2 × 3)ⁿ
According to Fundamental Theorem of Arithmetic, the factorisation is uniqe. It can be observed that 5 is not in the prime factorisation of 6ⁿ.
Hence, for any value of n, 6n will not be divisible by 5. Therefore, 6n cannot end with the digit 0 for any natural number n.
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If any digit has the last digit
10
that means it divisible by
10.
The factor of
10
=
2
×
5
,
So value of
6
n
should be divisible by
2
and
5.
Both
6
n
is divisible by
2
but not divisible by
5.
So, it can not end with
0.