Hello Natasha1 Originally Posted by

**Natasha1** Has anyone got a quick way to find the Highest Common Factor (HCF) of these numbers?

1). 6, 15

2). 12, 16

3). 12, 30

4). 21, 14

5). 36, 16

6). 50, 35

7). 45, 27

8). 64, 88

9). 35, 14

10). 20, 40

11). 28, 84

12). 48, 84

13). 99, 77

14). 90, 36

15). 60, 48

16). 88, 66

17). 96, 144

18). 140, 252

19). 175, 250

20). 396, 252

21). 27, 18, 99

22). 42, 56, 98

23). 108, 54, 90

24). 96, 192, 144

This is easier to do than to explain, but it's something like this:

1. Find the prime factors of each number.

2. For each prime factor that they have in common, choose the lower of their two exponents (powers).

3. Multiply these common factors together.

For instance, here's question 14, with the numbers $\displaystyle 90$ and $\displaystyle 36$:

$\displaystyle 90 = 2^1\times3^2\times 5^1$

$\displaystyle 36 = 2^2\times 3^2$

The common prime factors are $\displaystyle 2$ and $\displaystyle 3$; the lower of their exponents then are:

$\displaystyle 2^1$ and $\displaystyle 3^2$

So the HCF is $\displaystyle 2^1\times 3^2 = 18$.

Did you follow that?

Grandad