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Multiples
A multiple is the product of a number and an integer.
Let us take a number, 2, and multiply it by varying integers: 2x1 = 2, 2x2 = 4, 2x3=6...and so on.
2 is the selected number. It is being multiplied by integers(1, 2, 3...etc). The results(2, 4, 6...) are multiples of 2.
Integers can be positive, negative, or 0. Thus, 0, -2, -4 and -6 are also multiples of 2.
Common Multiples
A common multiple is a multiple that is shared by two or more numbers.
For example, 12 is divisble by both 3 and 4, so it is a common multiple of the two numbers.
15 is divisible by 5, but not 7, so 15 is not a common multiple of 5 and 7.
Factors
Factors are the numbers that are multipled together to get multiples.
6x4=24. 6 and 4 are the numbers multipled together, or factors, and 24 is the result.
The factors of 12 are: 1, 2, 3, 4, 6, and 12. Each of these numbers, when multipled by another number, produces 12: 1x12=12, 2x6=12, and 3x4=12.
Common Factors
Common factors are factors that are common to two or more numbers.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
It can be observed that the two numbers, 18 and 24, share certain factors, such as 1, 2, 3 and 6. These factors are common factors.