# Mathematics for GIS Professionals

Factors and Multiples

Factors

• [Factor]  a number or quantity that when multiplied with another produces a given number or expression e.g factors of 3 are 1 and 3 because $1\times 3 = 3$, $x$ and $y$ are factors of $3xy$
• [Multiple] a number  or expression that may be divided by another a certain number of times without a remainder e.g 10 is a multiple of 2 and 5, 200 is a multiple of 2, 4, 8 and 100. The expression $4x^{2}y$ is a multiple of $2, 4, x, x^2, y, xy$
• [Prime factor] a number that is divisble by only one and itself e.g $3, 7, 11, 13, 19, 23$

Factorisation is the process of decomposing a number or an expression into a product of its prime factors.

# Highest common factor and lowest common multiple

We can use prime factors to find the highest common factor (HCF) and lowest common multiple (LCM).

## Highest common factor

Here are the list of prime factors of 24 and 36:

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

If we write down the numbers that are the same in both lists, they will give us the highest common factor of 24 and 36:

HCF of 24 and 36 is 2 x 2 x 3 = 12

## Lowest common multiple

To find the lowest common multiple, we need to think about which list has the most of each factor.

24 = (2 x 2 x 2) x (3)

36 = (2 x 2)    x (3 x 3)

24 has the most 2s. (it has three 2s). And 36 has the most 3s (it has two 3s).

So the LCM of 24 and 36 is (2 x 2 x 2) x (3 x 3) = 72.

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