Greatest Common Factor Math Example 2

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

Example 2

medium
Find the GCF of 8484, 126126, and 210210.

Solution

  1. 1
    Prime factorizations: 84=22×3×784 = 2^2 \times 3 \times 7, 126=2×32×7126 = 2 \times 3^2 \times 7, 210=2×3×5×7210 = 2 \times 3 \times 5 \times 7.
  2. 2
    Common primes with minimum exponents: 21×31×71=422^1 \times 3^1 \times 7^1 = 42.
  3. 3
    The GCF of all three numbers is 4242.

Answer

4242
For three or more numbers, the process is the same: find the prime factorization of each, then take the lowest exponent for every prime that appears in all factorizations.

About Greatest Common Factor

The greatest common factor (GCF) of two or more numbers is the largest positive integer that divides each of them evenly, with no remainder. It is also called the greatest common divisor (GCD).

Learn more about Greatest Common Factor →

More Greatest Common Factor Examples

Example 1 easy

Find the GCF of [formula] and [formula].

Example 3 easy

Find the GCF of [formula] and [formula].

Example 4 easy

A teacher has ribbons of lengths [formula] cm and [formula] cm. She wants to cut them into the longe

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