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Find the greatest common factor

The greatest common factor (GCF) of two positive whole numbers is the largest factor shared by both numbers—that is, the largest whole number that divides each evenly. Finding it involves comparing factor pairs or factor lists and reasoning that no larger common factor exists; work focuses on pairs of numbers no greater than 100, supporting equal-grouping problems and later fraction simplification rather than generalized algebraic methods or large-number factorization.

Detailed Explanation: Find the greatest common factor

A factor is a whole number that divides another number evenly, with no remainder. To find the greatest common factor (GCF) of two numbers:

  1. List the factors of each number.
  2. Find the factors that appear in both lists.
  3. Choose the largest shared factor.

Example: Find the GCF of 2424 and 3636.

First, list the factor pairs of 2424:

1×24,2×12,3×8,4×61 \times 24,\quad 2 \times 12,\quad 3 \times 8,\quad 4 \times 6

So, the factors of 2424 are:

1, 2, 3, 4, 6, 8, 12, 241,\ 2,\ 3,\ 4,\ 6,\ 8,\ 12,\ 24

Now list the factor pairs of 3636:

1×36,2×18,3×12,4×9,6×61 \times 36,\quad 2 \times 18,\quad 3 \times 12,\quad 4 \times 9,\quad 6 \times 6

So, the factors of 3636 are:

1, 2, 3, 4, 6, 9, 12, 18, 361,\ 2,\ 3,\ 4,\ 6,\ 9,\ 12,\ 18,\ 36

The factors that both numbers share are:

1, 2, 3, 4, 6, 121,\ 2,\ 3,\ 4,\ 6,\ 12

The largest shared factor is 1212. Therefore,

GCF(24,36)=12\boxed{\text{GCF}(24,36)=12}

You can check: 24÷12=224 \div 12=2 and 36÷12=336 \div 12=3, so 1212 divides both numbers evenly.

Learn by doing: Find the greatest common factor

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