The number of factors of 3600 is:
45
Step 1 — Prime factorise 3600:
\(3600 = 2^4 \times 3^2 \times 5^2\)
Step 2 — Apply the divisor-count formula: If \(N = p_1^{a_1}p_2^{a_2}\cdots p_k^{a_k}\), the number of factors is \((a_1+1)(a_2+1)\cdots(a_k+1)\).
\(\text{Factors} = (4+1)(2+1)(2+1) = 5 \times 3 \times 3 = 45\)
Therefore 3600 has 45 factors.
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