Composite Numbers: Overview, Questions, Preparation

The composite numbers refer to those numbers with more than two factors, including the number 1 and itself. Simply, we can say that a composite number is a whole number that can be made by multiplying other whole numbers.

For example,- 8 (1, 2, 4, and 8) has more than two factors.

How to factorize the composite numbers (Prime Factorization)?

Remember that if the number is even, then it is divisible by 2, and if the sum of digits of integers is divisible by 3, then it is divisible by 3. If the end of the number is 0 or 5, then it is divisible by 5.

For example,

Let's take 126 is a composite number.

First, we divide it by 2; then we get 63

Again we divide the 63 by 3 and get 21

Again we divide the 21 by 3 and get 7

And 7 is a prime number.

So prime factors = 2 * 3 * 3 * 7

Types of Composite Numbers 

There are two types of composite numbers which are:

• Odd composite numbers
• Even composite numbers

Odd Composite Numbers

The odd composite numbers are those which have all the odd integers, not including the prime numbers. For example, 9, 15, 21, 27, 39 etc.

Even Composite Numbers

The even composite numbers are those which have all the even integers, not including the prime numbers. For example, 4, 6, 8, 10, 12, 14, 16, 18 etc.

The fundamental theorem of Arithmetic

This theory states that every composite number is a product of prime factorization. In simple words, we can say that,
Composite number = Products of primes

24 = 2 * 2 * 2 * 3

The chapter real numbers include the topic of composite numbers. The chapter discusses real numbers and their applications. The students learn about prime numbers, composite numbers, prime factorization, LCM, HCF, the fundamental theorem of Arithmetic, and many more in Class 10.
This chapter has a weightage of 6 marks in exams.

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

Solution.

At first, let’s take
7*11*13+13
Taking 13 as common factor,
13(7*11*1+1)
13(77+1)
13*78= 13*2*3*13
So, 7 * 11 * 13 + 13 is a composite number.

Now let's take other number
7 * 6 * 5 * 4 * 3 * 2 * 1 + 5
Taking 5 as a common factor,
5( 7*6*1*4*3*2*1+1)
5( 1008+1)
5 * 1009
So, 7 * 6 * 5 * 4 * 3 * 2 * 1 + 5 is a composite number.

2. Given that HCF (306, 657) = 9, find LCM (306, 657).

Solution.
HCF * LCM = Product of the two given numbers
So,
9 * LCM = 306 * 657
LCM = 306 * 657 / 9
LCM = 22338
LCM (306, 657) = 22338.

Q: Is 7 is a composite number?

Q: Find out the composite numbers between 1 and 20?

Q: What is the smallest composite number?

Q: How to determine composite numbers?

Q: Check whether 21 is a composite number or not?