Multiples and Factors Overview

Overview

This lecture explains the concepts of multiples and factors, how to identify them, and methods for quickly determining each.

Multiples of a number are the results of multiplying that number by whole numbers (its times table).
First five multiples of 6: 6, 12, 18, 24, 30.
All multiples of a number are divisible by that number with no remainder.
To check if a big number is a multiple, divide it by the number; if the result is whole, it's a multiple.
Example: 378 ÷ 6 = 63 (multiple), 412 ÷ 6 = 68.6 (not a multiple).
Multiples can also be found by repeatedly adding the number: 14, 28, 42, 56, etc. are multiples of 14.

Factors are whole numbers that can be multiplied together to get the original number (factor pairs).
Example factor pairs for 28: (1, 28), (2, 14), (4, 7).
All numbers in the factor pairs are factors of 28: 1, 2, 4, 7, 14, 28.
A factor divides the number exactly with zero remainder (e.g. 28 ÷ 4 = 7).
To list factors, write out all factor pairs starting with 1 × the number itself.
Example: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Example: Factors of 50 are 1, 2, 5, 10, 25, 50.

Multiples are larger numbers you get by multiplying (e.g. 12 → 24, 36, 48).
Factors are numbers that divide into the original number (e.g. 12 → 1, 2, 3, 4, 6, 12).
The number itself is always both a multiple and a factor.

Multiple — A number that can be produced by multiplying a given number by a whole number.
Factor — A whole number that divides another number exactly (no remainder).
Factor pair — Two whole numbers multiplied together to get the original number.