Question

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

Answer 1

Step 1: Explain the Composite numbers.

Composite numbers: Composite numbers also known as composites in mathematics are numbers that have more than $2$factors, not like prime numbers that have only two factor, i.e. $1$and 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 $\left(0\right)$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 $7\times 11\times 13+13$is composite number

We have, $7\times 11\times 13+13$

We can also write this as $(77+1)\times 13=74\times 13$

As $7\times 11\times 13+13=1014$ has more than two factors.

Hence, $7\times 11\times 13+13$ is a composite number. The given number

Step 3: Explain why $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ is composite number

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

As $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ has more than two factors.

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

Hence proved.