Can the number 6ⁿ, n being a natural number, end with the digit 5? Give reasons

Solution:

No,

Here 6ⁿ = (2 × 3)ⁿ = 2ⁿ × 3ⁿ ,

2 and 3 are the only primes in the factorisation of 6ⁿ, and not 5.

Therefore, it cannot end with the digit 5

✦ Try This: Can the number 4ⁿ, n being a natural number end with the digit 0? Give reasons

We know that any number is multiplied by 5 or 10 or by the multiples of 10 ends with zero.

Prime factorization of 4ⁿ can be expressed as = (2 × 2)ⁿ

If the number 4ⁿ, for any n were to end with o, it must be divisible by 5

That is prime factorization of 4ⁿ would contain the prime factor 5

4ⁿ = (2²)ⁿ = (2)²ⁿ

The only prime factor is 2

Therefore, the number 4ⁿ cannot end with the digit 0

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

NCERT Exemplar Class 10 Maths Exercise 1.2 Sample Problem 2

Can the number 6ⁿ, n being a natural number, end with the digit 5? Give reasons

Summary:

The number 6ⁿ, n being a natural number, cannot end with the digit 5

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