Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
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Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
Step-by-step explanation:
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.
So, basically there are two types of numbers i.e., prime numbers and composite numbers.
Understanding that, Prime numbers are those numbers having 1 and the number itself as factors.
Composite Number:-
Composite numbers are those numbers having factors other than 1 and itself.
It’s seen that,
7 x 11 x 13 + 13 = 13 x (7 x 11 + 1) [taking 13 out as common]
= 13 x (77 + 1)
= 13 x 78
= 13 x 13 x 6
So, the given expression has 6 and 13 as its factors. Therefore, we can conclude that it is a
Therefore, we can conclude that it is a composite number.
Similarly,
7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = 5 x (7 x 6 x 4 x 3 x 2 x 1 + 1) [taking 5 out- common]
= 5 x (1008 + 1)
= 5 x 1009
Since, 1009 is a prime number the given expression has 5 and 1009 as its factors other than 1 and
the number itself.
Hence, it is also a composite number.
THANKS!