Question

explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite number.​

Answer 1

Answer:

By definition,

A composite number is a positive integer that has a factor other than 1 and itself. Now considering your numbers,

7×11×13+13 may be written as, i.e. 13 * (78). So other than 1 and the number itself, 13 and 78 are also the factors of the number. Further, 78= 39 x 2. So, 39 and 2 are also it's factors. So this number is definitely not prime. Hence its composite number.

Similarly, 7×6×5×4×3×2×1+5 can be written as , i.e. 5 * (1009). So, other than the number and 1, it have 5 and 1009 as it's factors too. So it is also a composite number.

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Answer 2

Given,

$\:$

$\implies \sf \: 7×11×13+13 \: \: \& \: \: 7×6×5×4×3×2×1+5$

$\:$

$\implies \sf \: 13 \bigg(7×11×1+1 \bigg) \: \: \& \: \: 5 \bigg(7×6×1×4×3×2×1+1\bigg)$

$\:$

$\implies \sf \: 13 \bigg(77+1 \bigg) \: \: \& \: \: 5 \bigg(42×24+1\bigg)$

$\:$

$\implies \sf \: 13 \bigg(78 \bigg) \: \: \& \: \: 5 \bigg(1008+1\bigg)$

$\:$

$\implies \sf \: 1014\: \: \& \: \: 5045$

$\:$

∴ 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.

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