Find the greatest common factor

The greatest common factor of two or more positive whole numbers is the largest whole number that divides each quantity without a remainder; it can be determined by comparing factor lists or pairs and by identifying shared prime factors. This understanding supports simplifying fractions and factoring numerical expressions, including recognizing when one number is a factor of another; treatments involving zero, algebraic expressions, or polynomial factors are beyond this scope.

Detailed Explanation: Find the greatest common factor

A factor of a number divides it evenly, with no remainder. The greatest common factor (GCF) is the largest factor that two or more numbers share.

Example: Find the GCF of $24$ and $36$ .

Step 1: List the factors of each number.

Factors of $24$ :

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

Factors of $36$ :

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

Step 2: Identify the common factors.

The numbers that appear in both lists are:

1, 2, 3, 4, 6, 12

Step 3: Choose the greatest common factor.

The greatest number in the common-factor list is $12$ .

Therefore,

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

You can check that $12$ divides both numbers evenly:

24 \div 12=2 \qquad 36 \div 12=3

Learn by doing: Find the greatest common factor

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Finding Greatest Common Factor

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