Question

Find the HCF of the numbers in each of the following, using the prime factorization method:
72, 108, 180

Answer 1

The given numbers are 72, 108 and 180

We have:

$\begin{array}{l}2\overline{)\text{72}}\\ 2\overline{)\text{36}}\\ 2\overline{)\text{18}}\\ 3\overline{)\text{9}}\\ 3\overline{)\text{3}}\\ \text{1}\\ \end{array}$ $\begin{array}{l}2\overline{)\text{108}}\\ 2\overline{)\text{54}}\\ 3\overline{)\text{27}}\\ 3\overline{)\text{9}}\\ 3\overline{)\text{3}}\\ \text{1}\\ \end{array}$ $\begin{array}{l}2\overline{)\text{180}}\\ 2\overline{)\text{90}}\\ 3\overline{)\text{45}}\\ 3\overline{)\text{15}}\\ 5\overline{)\text{5}}\\ \text{1}\\ \end{array}$
Now, 72=2 × 2 × 2 × 3 × 3 = 2³ × 3²
108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³
180 = 2 × 2 × 3 ×3 × 5 = 2² × 3² × 5
∴ HCF =2²×3² =36