Q3 of 54 Page 8

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

If any number end with digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as

Prime factorization of 6n = (2×3)n


It can be observed that 5 is not in the prime factorization of 6n.


Hence, for an value of n, 6n will not visible by 5.


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


More from this chapter

All 54 →
1

Express each of the following number as a product of its prime factors.

(i) 140


(ii) 156


(iii) 3825


(iv) 5005


(v) 7429

 2

Find the LCM and HCF of the following integers by the prime factorization method.

(i) 12, 15 and 21


(ii) 17, 23 and 29


(iii) 8, 9 and 25


(iv) 72 and 108


(v) 306 and 657

 4

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

 5

How will you show that (17 × 11 × 2) + (17 × 11 × 5) is a composite number? Explain.