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.

By Ritesh|Updated : November 8th, 2022

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. Steps to prove 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:

Step 1: Explain the Composite numbers.

In contrast to prime numbers, which only have two factors—namely, 1 and the number itself—composite numbers, also known as composites in mathematics, have more than two factors.

  • Since they can be split by more than two integers, composite numbers are all natural numbers that are not prime numbers.
  • A composite number is any even number that is bigger than 2.
  • Given that it has no factors, zero is neither a prime nor a composite number.

Properties of Composite Numbers:

  • There are more than two components in composite numbers.
  • Every component of a composite number functions as a separate factor, and factors in composite numbers divide them equally.
  • 4, which is the smallest composite number.
  • At least two prime numbers will be included in each composite number's factors.
  • Additionally, composite numbers can be divided by other composite numbers.

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.

Comments

write a comment

CDS & Defence Exams

CDSCAPFAFCATTA ExamACC ExamOther ExamsPracticePreparation

Follow us for latest updates