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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 BYJU'S Exam Prep
Updated on: September 25th, 2023
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.
Table of content
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.