Factors Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
How many factors does 7272 have?

Solution

  1. 1
    Prime factorization: 72=23×3272 = 2^3 \times 3^2.
  2. 2
    The number of factors formula: (3+1)(2+1)=4×3=12(3+1)(2+1) = 4 \times 3 = 12.
  3. 3
    7272 has 1212 factors.

Answer

1212
If n=p1a1×p2a2×⋯n = p_1^{a_1} \times p_2^{a_2} \times \cdots, then the number of factors is (a1+1)(a2+1)⋯(a_1+1)(a_2+1)\cdots. This avoids listing every factor individually.

About Factors

Whole numbers that divide evenly into a given number with no remainder—the 'building blocks' that multiply together to make it.

Learn more about Factors →

More Factors Examples

Example 1 easy

List all factors of [formula].

Example 3 easy

Is [formula] divisible by [formula]? Explain using divisibility rules.

Example 4 easy

List all factor pairs of [formula].

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