Question

Prove the divisibility of the following numbers: 25^7+5^13 by 30

Answer 1

=5^14+5^13=(5+1)*5*5^12=30*5^12

Answer 2

The number $25^{7}+5^{13}$ is divisible by 30.

How to prove the divisibility of a given number by another number

In this question we must prove that a given number is divisible by another number, that is, the diviser is contained in the given expression. The demonstration is done by solely algebraically means:

$\frac{25^{7}+5^{13}}{30}$

$\frac{(5^{2})^{7}+5^{13}}{2 \times 3 \times 5 }$

$\frac{5^{14}+5^{13}}{2\times 3\times 5}$

$\frac{5^{13}\times (5+1)}{2\times 3\times 5}$

$\frac{5^{12}\times 5\times 2\times 3}{2\times 3 \times 5}$

$5^{12}$

Hence, the number $25^{7}+5^{13}$ is divisible by 30. $\blacksquare$

To learn more on divisibility, we kindly invite to check this verified question: https://brainly.com/question/369266