# Do the following numbers share common factors? If so, which is the greatest?: {70, 84, 105}

May 10, 2016

HCF = 7

#### Explanation:

For questions dealing with numbers, factors, LCM or HCF, prime, composite, squares, cubes etc, write the numbers as the product of their prime factors ... this tells you everything about the numbers.

$70 = 2 \times 5 \times 7 \text{ } 10 \times 7$
$84 = 2 \times 2 \times 3 \times 7 \text{ } 12 \times 7$
$105 = 3 \times 5 \times 7 \text{ } 5 \times 21$

In this form we can see that they all have the factor 7.
There is no other common factor so 7 is the HCF.