Question

Show that the following pairs are co-primes:
847, 1014

Answer 1

The given numbers are 847 and 1014.

$$\begin{gathered} \begin{array}{l}7\overline{)\text{847}}\\ 11\overline{)\text{121}}\\ 11\overline{)\text{11}}\end{array} \\ \overline{)\text{1}} \end{gathered}$$$$\begin{gathered} \begin{array}{l}2\overline{)\text{1014}}\\ 3\overline{)\text{507}}\\ 13\overline{)\text{169}}\\ 13\overline{)\text{13}}\end{array} \\ \overline{)\text{1}} \end{gathered}$$

847 = 7 × 11 × 11 × 1 = 7 × 11² × 1
1014 = 2 × 3 × 13 × 13 × 1
∴ HCF = 1
Hence, 847 and 1014 are co-primes.