Factors and multiples

The comprehension of factors and multiples must be understood to understand pre-algebraic relations.

Factors

A factor is a number that can be divided evenly into another given number without leaving a remainder. When a number fits the aforementioned definition, that number is called a factor of the given number.

For example,

• Since ${\displaystyle 7*2=14}$, 7 and 2 are both factors of 14.
• Since ${\displaystyle {\frac {30}{6}}\ =5}$, 6 and 5 are factors of 30.

Factors come in handy when simplifying equations. The highest factor of a number will always be the number itself and the lowest factor of a number will always be 1.

Multiples

A multiple is when we multiply one given whole number by another whole number. When a number fits the aforementioned definition, that number is called a multiple of the given number.

For example,

• If our given number is 3 and we multiply it by 3, which equals 9, 9 will be a multiple of 3.
• If our given number is 10 and we multiply it by 2, which equals 20, 20 will be a multiple of 10.
• The first three multiples of 4 are 4, 8, 12.
• The first three multiples of 11 are 11, 22, 33.

We could never list out all of the multiples for every number, as it would be infinite. But multiples give us a good understanding of our multiplication tables.