Question

Explain why 7X11×13+13 and 7 x 6 x 5x 4 x3 ×2 ×1 +5
are composite numbers.​

Answer 1

Here is ur answer mate

7×11×13+13

13(7×11×1+1)

13(77+1)

(13×78)

This shows that given number has more than two factors. Hence it is a composite number

7×6×5×4×3×2×1+5

5(7×6×1×4×3×1+1)

5(42×12+1)

5(42×13)

(5×546)

This shows that given number has more than two factors. Hence it is a composite number

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Answer 2

Let us represent the first number as X.

Then X = 7 x 11 x 13 + 13

Composite number is a number which has positive divisors other than one and itself.

Now,

X can be written as:

X = ( 7 x 11 + 1) x 13 ..( taking 13 as common)

= 78 x 13

Hence we can represent X as a product of two divisors greater than one.

therefore, X is a composite Number.

Now similarly the other number can be written as:

Y = 7 x 6 x 5 x 4x 3x 2x 1 + 5

= ( 7 x 6 x 4 x 3x 2 x 1 + 1 ) x 5

= 1009 x 5

Hence Both are composite numbers.

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