Question

Find the HCF of the numbers in each of the following, using the prime factorization method:
1197, 5320, 4389

Answer 1

The given numbers are 1197, 5320 and 4389.

We have:

$\begin{array}{l}3\overline{)\text{1197}}\\ 3\overline{)\text{399}}\\ 7\overline{)\text{133}}\\ 19\overline{)\text{19}}\\ \text{1}\\ \end{array}$ $\begin{array}{l}2\overline{)\text{5320}}\\ 2\overline{)\text{2660}}\\ 2\overline{)\text{1330}}\\ 5\overline{)\text{665}}\\ 7\overline{)\text{133}}\\ 19\overline{)\text{19}}\\ \text{1}\\ \end{array}$ $\begin{array}{l}3\overline{)\text{4389}}\\ 7\overline{)\text{1463}}\\ 19\overline{)\text{209}}\\ 11\overline{)\text{11}}\\ \text{1}\end{array}$
Now, 1197 = 3 × 3× 7× 19 = 3² × 7 × 19
5320 = 2 × 2 × 2× 5 × 7 × 19 = 2³ × 5 × 7 × 19
4389 = 3 ×7 × 19 × 11
∴ Required HCF = 19 × 7 = 133