Question

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

Answer 1

7×11×13+13 may be written as, 13x{(7x11) + 1} i.e. 13x(78). So other than 1 and the number itself, 13 and 78 are also the factors of the number. Further, 78=39x2. 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 5x{(7x6x4x3x2x1)+1}, i.e. 5x(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.

Hope this helps!

Answer 2

✨$\huge\red{\boxed{\underline{\bf Answer}}}$

By definition,

A composite no. is a positive integer that has a factor other than 1 and itself. Now, considering your no.

$\bf{7 \times 11 \times 13 + 13}$ may be written as, $\bf{13 \times [(7 \times 11) + 1]}$ that is $\bf{13 \times (78)}$.

So, other than 1 and the no. itself, 13 and 78 are also the factor of the no.

Further, $\bf{78 = 39 \times 2}$ So, 39 and 2 are also it's factor. So, this no. is not prime, it is composite.

Similarly, $\bf{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5}$ can be written as $\bf{5 \times [(7 \times 6 \times 4 \times 3 \times 2 \times 1) + 1]}$ that is $\bf{5 \times (1009)}$. So, other than the number and 1, it have 5 and 1009 as it's factors too. So it is also a composite number

$\huge\boxed{\bf Verified}$