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Tell whether the following statement is true or false:

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

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True

False

answer is A.

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Detailed Solution

Given the numbers 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5.
If the number has prime factors other than 1 then they will be composite.
Checking the prime factors of

7 × 11 × 13 + 13

= 13 (7 × 11 + 1) = 13 (77 + 1) = 13 × 78 = 13 × 13 × 3 × 2

Hence, it is a composite number.
Checking the prime factors of

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

= 5 7 × 6 × 4 × 3 × 2 × 1 + 1 = 5 1008 + 1 = 5 × 1009

Hence, it is a composite number.
Therefore, the given statement is true.
Hence, option 1 is correct.

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