Step 2: Explain why 7 x 11 x 13 + 13 is composite number
We have 7 x 11 x 13 + 13
We can also write this as (77 + 1) x 13 = 74 x 13
As 7 x 11 x 13 + 13 = 1014 has more than two factors.
Hence, 7 x 11 x 13 + 13 is a composite number.
Step 3: Explain why 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 is composite number
We can also write it as 5 (7 x 6 x 5 x 4 x 3 x 2 x 1 + 1) = 1009 x 5
As 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 has more than two factors
Hence, 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 is also a composite number
Therefore, proved.
Summary:
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.
It is proved that 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers. In a composite number, there are more than two components. The smallest composite number is 4.
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