If n is any natural number, then 5^{2n}-1 is <strong>ALWAYS</strong> divisible by how many natural numbers?

Explanation

For n=1, 5^2-1 = 24. Since 5^{2n}-1 = 25^n - 1^n, it is always divisible by 25-1=24. The number 24 has prime factorization 2^3 \times 3^1. The total number of factors is (3+1)(1+1) = 8.

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