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Question

Explain why 7×11×13+13and 7×6×5×4×3×2×1+5 are composite numbers?


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Solution

Step 1: Explain the Composite numbers.

Composite numbers: Composite numbers also known as composites in mathematics are numbers that have more than 2factors, not like prime numbers that have only two factor, i.e. 1and the number itself.

  • Composite numbers are all natural numbers that are not prime numbers since they can be divided by more than two numbers.
  • Any even number which is greater than 2 is a composite number.
  • Zero (0)is considered neither prime nor a composite number because it does not have any factors

Properties of Composite Numbers:

  • Composite numbers have more than two factors
  • Each composite number is a factor in itself
  • Composite numbers are evenly divisible by their factors
  • The smallest composite number is 4
  • Each composite number will include at least two prime numbers as its factors.
  • Composite numbers are divisible by other composite numbers also.

Step 2: Explain why 7×11×13+13is composite number

We have, 7×11×13+13

We can also write this as (77+1)×13=74×13

As 7×11×13+13=1014 has more than two factors.

Hence, 7×11×13+13 is a composite number. The given number

Step 3: Explain why 7×6×5×4×3×2×1+5 is composite number

We can also write it as 5(7×6×5×4×3×2×1+1)=1009×5

As 7×6×5×4×3×2×1+5 has more than two factors.

Hence, 7×6×5×4×3×2×1+5 is also a composite number.

Hence proved.


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