Factors and Multiples

If a number x divides another number y exactly (without leaving any remainder), then x is a factor of y and y is a multiple of x.

or

Factors  Set of numbers which exactly divides the given number.

Multiple  Set of numbers which are exactly divisible by the given number.

For example If the number is 8, then {8, 4, 2, 1} is the set of factors, while { 8, 16, 24, 32, ......} is the set of multiple of 8.

Note

1. Factors of a number are always less than or equal to the given number.
2. Multiples of a number are always more than or equal to the given number.

Common Multiple

A common multiple of two or more numbers is a number which is completely divisible (without leaving remainder) by each of them.

For example We can obtain common multiples of 3, 5 and 10 as follows

Multiple of 3

       = {3, 6, 9,12, 15, 18, 21, 24, 27, 30, 33 ....}

Multiples of 5 = { 5, 10, 15, 20, 25, 30 ,35, ....}

Multiples of 10 = { 10, 20, 30, 40, 50, 60, ....}

Common multiples of 3, 5 and 10
                            = { 30, 60, 90, 120 ....}