Question

If the prime factorisation of a natural number n is 2⁴ × 3⁴ × 5³ × 7, then the number of consecutive zeros in n, is _________.

Answer 1

To calculate the number of consecutive zeros, we need to find the number of pairs of 2 and 5 to form a product of 10.

Here, n = 2⁴ × 3⁴ × 5³ × 7
= 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5 × 7
= 2 × 5 × 2 × 5 × 2 × 5 × 2 × 3 × 3 × 3 ×​ 3 × 7
= 10 × 10 × 10 × 2 × 3 × 3 × 3 ×​ 3 × 7
= 2 × 3⁴ × 7 × 10³

Hence, the number of consecutive zeros in n, is 3 .