Review factors and multiples, and try some practice problems.

What is a factor?

A factor is a whole number that can divide evenly into another number.
The factors of 8\purpleD8 are: 1,2,4,\blueD{1, 2, 4}, and 8\blueD8.
8÷1=8\purpleD8 \div \blueD1 = 8
8÷2=4\purpleD8 \div \blueD2 = 4
8÷4=2\purple8 \div \blueD4 = 2
8÷8=1\purpleD8 \div \blueD8 = 1
1,2,4,\blueD{1, 2, 4}, and 8\blueD8 all divide evenly into 8\purpleD8.

Factor pairs

A factor pair is 22 whole numbers that can be multiplied to get a certain product.
The factor pairs of 8\pink{\purpleD8} are:
1\blueD1 and 8\blueD8 because 1×8=8\blueD1 \times \blueD8 = \pink{\purpleD8}
2\blueD2 and 4\blueD4 because 2×4=8\blueD2 \times \blueD4 = \purpleD{8}
Want to learn more about finding factors? Check out this video.
Want more ways to think about factors and multiples? Check out this article.

Practice set 1: Finding factors

Problem 1A
Which of the following numbers is a factor of 7878?
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Want to try more problems like this? Check out this exercise.

What is a multiple?

A multiple is a number that results when we multiply one whole number by another whole number. The first four multiples of 3\blueD{3} are 3,6,93, 6, 9, and 1212 because:
3×1=3\blueD{3} \times 1 = 3
3×2=6\blueD{3} \times 2 = 6
3×3=9\blueD{3} \times 3 = 9
3×4=12\blueD{3} \times 4 = 12
Some other multiples of 3\blueD{3} are 15,3015, 30 and 300300.
3×5=15\blueD{3} \times 5 = 15
3×10=30\blueD{3} \times 10 = 30
3×100=300\blueD{3} \times 100 = 300
We can never list all of the multiples of a number. In our example, 3\blueD3 could be multiplied by an infinite number of numbers to find new multiples.

Identifying multiples

We can check to see if a number is a multiple of another number by seeing if it can be divided evenly by the number.
1515 is a multiple of 3\blueD3 because 15÷3=515 \div \blueD3 = 5.
1717 is not a multiple of 3\blueD3 because 17÷3=5 R 217 \div \blueD3 = 5 \text{ R } 2.
Want to learn more about finding factors and multiples of a number? Check out this video.

Practice set 2: Finding multiples

Problem 2A
Which of the following numbers is a multiple of 99?
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Want to try more problems like this? Check out this exercise.