Question

find the HCF of the following by prime factorisation method:problem 315,540?

Answer 1

$315 = 3 \times 105 \\ \: \: \: \: \: \: \: \: = 3 \times 3 \times 35 \\ \: \: \: \: \: \: \: \: = 3 \times 3 \times 5 \times 7 \\ 540 = 2 \times 270 \\ \: \: \: \: \: \: \: \: = 2 \times 2 \times 135 \\ \: \: \: \: \: \: \: \: = 2 \times 2 \times 3 \times 45 \\ \: \: \: \: \: \: \: \: \: = 2 \times 2 \times 3 \times 3 \times 15 \\ \: \: \: \: \: \: \: \: \: \: = 2 \times 2 \times 3 \times 3 \times 3 \times 5 \\ common \: factor \: of \: both \: means \: 315 \: and \: 540 \: are \:3 \: 3 \: 5 \\ multiply \: of \: those \: common \:factor \: = 3 \times 3 \times 5 = 45 \\ the \: hcf \: is \: 45$