Question

Find the HCF of the numbers in each of the following, using the prime factorization method:
504, 980

Answer 1

The given numbers are 504 and 980.

We have:

$\begin{array}{l}2\overline{)\text{504}}\\ 2\overline{)\text{252}}\\ 2\overline{)\text{126}}\\ 3\overline{)\text{63}}\\ 3\overline{)\text{21}}\\ 7\overline{)\text{7}}\\ \text{1}\\ \end{array}$ $\begin{array}{l}2\overline{)\text{980}}\\ 2\overline{)\text{490}}\\ 5\overline{)\text{245}}\\ 7\overline{)\text{49}}\\ 7\overline{)\text{7}}\\ \text{1}\\ \end{array}$

504 = 2 × 2 ×2 × 3 × 3 × 7 = 2³ × 3² × 7
980 = 2 × 2 × 5× 7 × 7 = 2² × 5 × 7²
∴ HCF of the given numbers = 2² × 7 = 28