# Multiple

A multiple of a whole number is the product of that whole number and another whole number. When someone says that a number is a multiple of another number, it means that the other number can be multiplied by an integer to form the first number; 4 is a multiple of 2 because 2 × 2 = 4, but 4 is not a multiple of 3 because 3 cannot be multiplied by an integer to get a result of 4 (3 × 1.33 = 4).

Examples
Multiples of 4 include 0, 4, 8, 12,...
 (0 × 4 = 0; 1 × 4 = 4; 2 × 4 = 8; 3 × 4 = 12)
Multiples of 6 include 0, 6, 12, 18,...
 (0 × 6 = 0; 1 × 6 = 6; 2 × 6 = 12; 3 × 6 = 18)

### Properties of multiples

• 0 is a multiple of everything, since zero multiplied by any number is still zero.
• Every integer is a multiple of itself because anything multiplied by 1 is the same number. So any integer can be multiplied by 1 to result in said integer, making it a multiple of itself.
• The product of an integer, n, and any integer, is a multiple of n. This should make sense because it fits the definition of what a multiple is, described above.
• If two integers, designated A and B, are a multiple of another number, n, then A + B and A - B are also multiples of n.
• Example: 4 and 8 are multiples of 2. 8 + 4 = 12; 8 - 4 = 4. Both 4 and 12 are also multiples of 2.