Check whether 6ⁿ can end with the digit 0 for any natural number n

Solution:

If any number ends with the digit 0 that means it should be divisible by 5. That is, if 6ⁿ ends with the digit 0, then the prime factorisation of 6ⁿ would contain the prime number 5.

Prime factors of 6ⁿ = (2 × 3)ⁿ = (2)ⁿ × (3)ⁿ

We can clearly observe, 5 is not present in the prime factors of 6ⁿ. That means 6ⁿ will not be divisible by 5.

Therefore, 6ⁿ cannot end with the digit 0 for any natural number n.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 1

Video Solution:

Check whether 6ⁿ can end with the digit 0 for any natural number n.

NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.2 Question 5

Summary:

The number 6ⁿ cannot end with the digit 0 for any natural number n as 5 is not present in the prime factors of 6ⁿ.

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