Find common factors

Common factors are whole numbers that divide each of two given whole numbers evenly, leaving no remainder; for numbers within 100, they can be identified by listing factor pairs or using multiplication facts and arrays to reveal shared grouping structures. This understanding distinguishes common factors from common multiples and supports later work with divisibility and equivalent fractions, without requiring prime factorization, algebraic generalization, or factors of larger or more general numbers.

Detailed Explanation: Find common factors

A common factor is a whole number that divides evenly into two numbers.

To find common factors:

List the factor pairs for the first number.
List the factor pairs for the second number.
Find the numbers that appear in both lists.

Example: Find the common factors of $18$ and $24$ .

Step 1: List the factor pairs of $18$ .

1 \times 18=18

2 \times 9=18

3 \times 6=18

So, the factors of $18$ are:

1,\ 2,\ 3,\ 6,\ 9,\ 18

Step 2: List the factor pairs of $24$ .

1 \times 24=24

2 \times 12=24

3 \times 8=24

4 \times 6=24

So, the factors of $24$ are:

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

Step 3: Find the factors in both lists.

The numbers that appear in both lists are:

\boxed{1,\ 2,\ 3,\ 6}

Therefore, the common factors of $18$ and $24$ are $\boxed{1, 2, 3, \text{ and } 6}$ . Each one divides both numbers evenly, with no remainder.

Learn by doing: Find common factors

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Finding Greatest Common Factor

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