**Amazing Composite Numbers**

In this article, we will learn the definition of composite numbers, their properties, the smallest number, the even and odd numbers, a list of composite numbers, and the difference between along with many solved examples in detail. Let’s start by knowing what it is a composite number?

A composite number is a natural number or a positive integer which has more than two factors. For example, 14 has factors 1, 2, 7, And the same, 15 has factors 1, 3, 5, and 15; hence all are composite number.

Number 4 has factors 1, 2, 4; hence it is a composite number. We know that a **prime number **is a whole number with exactly two integral divisors, 1 and itself.

#### Definition

Composite Numbers : A positive integer with factors other than 1 and itself. A number that is not prime.

Examples of Composite Numbers: | Examples of Prime Numbers: |

4 has factors 1, 2, 4 | 3 has factors 1, 3 |

8 has factors 1, 2, 4, 8 | 5 has factors 1, 5 |

24 has factors 1, 2, 3, 4, 6, 8, 12, 24 | 13 has factors 1, 13 |

15 has factors 1, 3, 5, 15 | 23 has factors 1, 23 |

Composites has factors other than 1 and itself. The first few composite numbers (sometimes called “composites” for short) are 4,6,8,10,12,14,15, 16,

Is 19 a composite number?

No, since 19 has only two factors, i.e. 1 and 19. In other words, 19 is not a composite number because 19 doesn’t have more than 2 factors.19 is a prime number.

We note that all these numbers have more than two factors. Numbers can be classified on the basis of the number of factors that they have. If a number has just two factors – 1 and the number itself, then it is a prime number. However, most numbers have more than two factors,

Number | Factors | No. of factors | The number |

1 | 1 | 1 | Not prime, not composite |

2 | 1,2 | 2 | Prime number |

4 | 1,2,4 | 3 | Composite number |

6 | 1,2,3,6 | 4 | Composite number |

7 | 1,7 | 2 | Prime number |

9 | 1,3,9 | 3 | Composite number |

**It** can be defined as natural numbers that have more than two factors. In other words, a number that is divisible by a number other than 1 and the number itself, is called a composite number. Let us learn more about composite numbers with examples.

4, 6, 8, 9, and 10 are the first few composite numbers. Let us take 4 and 6. In the above example, 4 and 6 are called each composite number .

## **What are Composite Numbers in Math?**

In Mathematics, **composite numbers** are numbers that have more than two factors. These numbers are also called composites. Composite numbers are just the opposite of the prim numbers which have only two factors, i.e. 1 and the number itself.

All the natural numbers which are not prime numbers are composite as they can be divided by more than two numbers. For example, 6 is a composite number because it is divisible by 1, 2, and 3 and even by 6.

So, a whole number can be made by multiplying other whole numbers.

Example: 6 can be made by 2 × 3 so is a composite number.

But 13cannot be made by multiplying other whole numbers (1×13 would work, but we said to use other whole numbers). So, it is not a composite number. It is a prime number.

Fact: Any even number which is greater than 2 is a composite number.

## How to Find Composite Numbers?

In order to find a composite number, we find the factors of the given number. If the number has more than two factors, then it is composite. The best way to figure out a composite number is to perform the divisibility test. The divisibility test helps us to determine whether a number is a prime or a composite number.

Divisibility means that a number is divided completely (with no remainder) by another number. To do this, check to see if the number can be divided by these common factors: 2, 3, 5, 7, 11, and 13. If the given number is even, then start checking with the number 2. If the number ends with a 0 or 5, then check it by 5.

If the number cannot be divided by any of these given numbers, then the number is a prime number. For example, 68 is divisible by 2, which means it has factors other than 1 and 68. So, we can say 68 is a composite number.

For example, number 12 is divisible by 2, 3, 4, 6 which means it has factors other than 1 and 12. So, we can say that 12 is a composite number, but number 11 has only two factors, 1 and 11. In other words, 11 is not a composite number because 11don’t have more than 2 factors. Therefore,11 is a prime number.

## ** Examples**:

The examples of composite numbers are 25, 30, 52, 64, est., such that:

Composite number | Factors |

25 | 1,5,25 |

30 | 1,2,3,5,6,10,15,30 |

52 | 1,2,4,13,26,52 |

64 | 1,2,4,8,64 |

In all the above examples, we can see that the composite numbers have more than two factors. There are a number of composite numbers we can list out of a set of natural numbers from 1 to 1000 or more.

**Properties of Composite Numbers**

The properties of composite numbers are easy to remember.

- Composite numbers have more than two factors
- Composite numbers are evenly divisible by their factors
- Each composite number is a factor of itself
- The smallest composite number is number 4
- Each composite number will include at least two prime numbers as its factors (10 = 2 x 5, where 2 and 5 are prime numbers)
- Composite numbers are divisible by other composite numbers

In other words, composite numbers have factors other than 1 and itself. For example, number 6 is a composite number because it has 1, 2, 3, and 6 as its factors.

## **How do you find a Composite Number?**

Follow these steps:

- Find all factors of the number.
- If the number has only two factors, 1 and itself, then the number is prime.
- If the number has more than two factors, then the number is composite.

## **How do you know which Tests to perform?**

- If a number less than 121 and it isn’t divisible by 2, 3, 5, or7, then it’s a prime number, otherwise, it’s a composite number.
- If a number is less than 289 and it isn’t divisible by 2, 3, 5, 7, 11, or 13, then it’s a prime number; otherwise, it’s a composite number.

As we know a prime number is a whole number with exactly two integral divisors, 1 and itself. And a composite number is a whole number with more than two integral divisors. So, all whole numbers (except 0 and 1) are either prime or composite.

All even numbers are composite numbers. Since composite numbers are those which have factors other than 1 and the number itself. Yes, we can say that all the even numbers, except 2, are composite numbers since they have factors other than 1 and the number itself.

**What is a Composite Number?**

A composite number is a natural number or a positive integer which has more than two factors.

For example, 15 has factors 1, 3, 5, and 15, hence it is a composite number.

Example: Find if 14 is a composite number. Let us find the factors of 14.

14÷1 = 14, 14÷2 = 7, 14÷7 = 2, 14÷14 = 1

As we can see, the factors of 14 are 1, 2, 7, and 14, so it is a composite number.

Repeat again, a composite number is a positive integer that can be formed by multiplying two smaller positive integers. Note the properties of a composite number listed below:

- All composite numbers are evenly divisible by smaller numbers that can be prime or composite
- Every composite number is made up of two or more prime numbers

**Find Composite Numbers 1 – 100:**

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

## **Types of Composite Numbers**

There are two main types of composite numbers in Math’s which are:

- Odd Composite Numbers or Composite Odd Numbers
- Even Composite Numbers or Composite Even Numbers
- One is not a prime or composite number.
- Two is the only even prime number.
- Not all Odd numbers are prime.(example: 9, 15, 21, 27, 33, 35, …)
- All composite numbers can be written as product of prime numbers.

## **Odd Composite Numbers**

All the odd integers which are not prime are odd composite numbers. Examples of composite odd numbers are 9, 15, 21, 25, 27, 31, etc. We note that 1, 3, 5, 7, all are odd numbers, but they are not composite numbers.

## **Even Composite Numbers**

All the even numbers which are not prime are even composite numbers. For example, 4, 6, 8, 10, 12, 14, 16, are even composite numbers. Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12 and 15 again. Here 4, 10, and 12 are the even composites because they have even divisors and they fulfill the conditions of composite numbers.

** Smallest Composite Numbers **

A composite number is defined as a number that has divisors other than 1 and the number itself. Now, as we start counting: 1, 2, 3, 4, 5, 6, so on, we see that 1 is not a composite number because its only divisor is 1. 2 is not a composite number as well because it has only two divisors, 1 and the number 2 itself.

3 is not a composite number because it has only two divisors, 1 and the number 3 itself. However, when we come at number 4, we know that its divisors are 1, 2, and 4. Number 4 satisfies the criteria of a composite number. So, 4 is the smallest composite number.

### **Important Notes on Composite Numbers**

- Smallest Composite Number is 4
- Smallest Prime Number is 2
- Smallest Odd Composite Number is 9
- Two-digit Smallest Composite Number is 10

### **Solved Problems on Composite Numbers**

Example 1:

What is the prime factorization of 60? Are 60 is a composite number?

Solution: The prime factorization of 60 is: 60 = 2 × 2 × 3 × 5.

Yes, 60 is a composite number.

Example 2: Find if 164 is a composite number.

Solution:

The factors of 164 are 1, 2, 4, 8, 41, 82, and 164.

Therefore, 164 is a composite number.

Example 3:

List out the composite numbers from the given set of numbers.

2, 4, 9, 11, 21, 31, 44, 51, 53.

Solution:

The composite numbers are 4, 9, 21, 44and51.

**Practice Questions (Worksheet)**

Do by yourself:

- List the composite numbers between 20 and 50.
- Find if 85 is a composite number.
- What are the prime factors of 99?

This was all about Composite Numbers. We hope you enjoyed it. To practice even more, on different numbers and learn about other interesting mathematics’ concepts, keep visiting LearningMole.