The factors of a given number are those numbers which divide into the given number exactly without any remainder.
The multiples of a given number are those numbers into which the given number divides exactly with no remainder (that is the given number's times table).
example
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 since they all divide into 60 without any remainder
The multiples of 60 are: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, (and so on) since they are all divisible by 60 with no remainder.
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Factors go into numbers, numbers go into multiples.
Common factors go into the numbers, the numbers go into common multiples.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 The multiples of 24 are 24, 48, 72 and so on.
Factors of the number will also be factors of the number's multiples. Multiples of the number will also be multiples of the number's factors.
Factors go into numbers, numbers go into multiples.