Question

Which of the following options lists all the prime factors of 8^17-8^15 ? ​

Answer 1

${2}^{45} \times {3}^{2} \times 7$

Step-by-step explanation:

$Given, \: \: \: {8}^{17} - {8}^{15} \\ \: \: \: \: \: \: = {8}^{15} ( {8}^{2} - 1) \\ \: \: \: \: \: \: = {8}^{15} (64 - 1) \\ = {8}^{15} \times 63 \\ \: \: \: \: \: \: \: \: \: \: \: = ( {2}^{3} )^{15} \times 9 \times 7 \\ \: \: \: \: \: \: \: = \boxed{{2}^{45} \times {3}^{2} \times 7}$