Question

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

Answer 1

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 xx 5 xx 7 " " 10 xx 7`
`84 = 2 xx 2 xx 3 xx 7 " " 12 xx 7`
`105 = 3 xx 5 xx 7 " " 5 xx 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.