# Check whether 6^{n} 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 6^{n} ends with the digit 0, then the prime factorisation of 6^{n} would contain the prime number 5.

Prime factors of 6^{n} = (2 × 3)^{n} = (2)^{n }× (3)^{n}

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

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

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

**Video Solution:**

## Check whether 6^{n} 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 6^{n} cannot end with the digit 0 for any natural number n as 5 is not present in the prime factors of 6^{n}.

**☛ Related Questions:**

- Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
- Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
- Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25
- Given that HCF (306, 657) = 9, find LCM (306, 657).

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