Question

Explain why ( 7 x 13 x11 + 11 ) and ( 7 x 6 x 5 x 4 x 3 x 2 x 1+ 7 ) are a composite number
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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, 13 * [(7 * 11) + 1]13∗[(7∗11)+1] 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 5*[(7*6*4*3*2*1) + 1]5∗[(7∗6∗4∗3∗2∗1)+1] , 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.

Answer 2

Answer:

ANSWER

Given 7×11×13+13

=13×(7×11+1)=3×78

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.

similarly in

7×6×5×4×3 ×2×1+5

=5(7×6×4×3 ×2×1+1)=5×1009

This number is multiple of two integers.Hence it has more than two factors.Hence it is a composite number.