Question

Answer this question tenth class students. Thank you ​

Answer 1

Question :-

Explain why $7 \times 11 \times 13 + 13$and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$are composite numbers.

Answer :-

$7 \times 11 \times 13 + 13$

$= 13 \: ( \: 7 \times 11 + 1 \: )$

$= 13 \times (77 + 1)$

$= 13 \times 78$

$= 13 \times 13 \times 3 \times 2$

Since, it has more than two factors $(13 \:, 3 \:, 2 \:, 1 \:, 13 \times 78 \: \: i.e. \: 1014)$, it is a composite number.

Now,

$7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$

$= 5 \: (7 \times 6 \times 4 \times 3 \times 2 \times 1 + 1)$

$= 5 \: (1008 + 1)$

$= 5 (1009)$

Since, it has more than two factors $(5 \:, 1009 \:, 1 \:, 5 \times 1009 \: \: i.e. \: 5045)$,it is a composite number.