Question

Show that the following pairs are co-primes:
161, 192

Answer 1

The given numbers are 161 and 192.
We have:
$$\begin{gathered} \begin{array}{l}7\overline{)161}\\ 23\overline{)23}\end{array} \\ \overline{)1} \end{gathered}$$ $\begin{array}{l}2\overline{)192}\\ 2\overline{)\text{96}}\\ 2\overline{)\text{48}}\\ 2\overline{)\text{24}}\\ 2\overline{)12}\\ 2\overline{)\text{6}}\\ 3\\ \end{array}$

Now, 161 = 7 × 23 × 1
192 = 2 × 2× 2 ×2 × 2× 2 × 3 = 2⁶ × 3 × 1
∴ HCF = 1
Hence, 161 and 192 are co-primes.