[Math Lair] Factors and Multiples

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A number that divides an exact number of times into another number is said to be a factor, sub-multiple or measure of the latter number. For example, 15 = 3 × 5, so both 3 and 5 are factors of 15.

A number that, when divided by another number, leaves no remainder, is said to be a multiple of the latter number. For example, 15 ÷ 3 = 5, so 15 is a multiple of 3 (and 5).

By the Fundamental Theorem of Arithmetic, every natural number greater than 1 can be factored into prime numbers in one way and one way only.

The Least Common Multiple of two or more numbers is the smallest number that is a multiple of each number.

The Greatest Common Divisor (also known as Greatest Common Factor or Greatest Common Measure) of two or more numbers is the greatest number contained an exact number of times in each number.