How do you identify a composite number?
How do you identify a composite number?
Mathematics is one of the most interesting concepts that the students often come across. We will be able to understand the basic concepts once we are being able to understand the application of the same as well. so, in the field of mathematics, the composite numbers can be defined as numbers that have more than two factors, unlike prime numbers which have only two factors, i.e., 1 and the number itself. These numbers are also called composites.
In this case, we will see that all the natural numbers which are not prime numbers are composite numbers and so they can be divided by more than two numbers. If we are to take an example, 8are composite because it is divisible by 1, 2, and 4 such as:
- 8÷1 = 8
- 8÷2 = 4
- 8÷4 = 2
The integers which can be generated with the help of multiplication of two smallest positive integers and also contain at least one divisor other than number ‘1’ and itself are composite numbers. These numbers always have more than two factors.
Fact: Any even number which proves to be greater than 2 is a composite number.
How to Determine the Composite Number?
This is one of the most important steps that we should determine as to how will we be able to determine the composite number? There are always a few steps that are to be followed when we want to understand the procedures of a composite number.
- The first step is to find all the factors of the positive integer
- We can say that the number is a prime if it has only two factors, 1 and itself.
- But on the other hand, if we have a numberthat has more than two factors, then it is a composite.
Example: Find if 14 is a composite number.
Let us find the factors of 16.
- 16÷1 = 16
- 16÷2 = 8
- 16÷8 = 2
- 16÷16 = 1
As we can see, the factors of 16can be divided by 2, 8, 1 and the number itself therefore it is a composite number.
List of Composite Numbers
So, here we can safely say that the numbers are positive integers and that they will get divided by other numbers as well. The list of composite numbers up to 150 is:
4 | 28 | 50 | 70 | 91 | 112 | 130 | 150 |
6 | 30 | 51 | 72 | 92 | 114 | 132 | |
8 | 32 | 52 | 74 | 93 | 115 | 133 | |
9 | 33 | 54 | 75 | 94 | 116 | 134 | |
10 | 34 | 55 | 76 | 95 | 117 | 135 | |
12 | 35 | 56 | 77 | 96 | 118 | 136 | |
14 | 36 | 57 | 78 | 98 | 119 | 138 | |
15 | 38 | 58 | 80 | 99 | 120 | 140 | |
16 | 39 | 60 | 81 | 100 | 121 | 141 | |
18 | 40 | 62 | 82 | 102 | 122 | 142 | |
20 | 42 | 63 | 84 | 104 | 123 | 143 | |
21 | 44 | 64 | 85 | 105 | 124 | 144 | |
22 | 45 | 65 | 86 | 106 | 125 | 145 | |
24 | 46 | 66 | 87 | 108 | 126 | 146 | |
25 | 48 | 68 | 88 | 110 | 128 | 147 | |
27 | 49 | 69 | 90 | 111 | 129 | 148 |
So, this is so very important that we should be able to understand as to what all are the process that will be followed. Here are a few steps that will help us identify the numbers:
- Let us assume here that the number N that will be called a prime if it can undergo complete division (remainder =0) and is only left with 1 and itself. Here for example, 7 is a prime number because if we want to have a look at the numbers that can completely divide 7 then we will only find 1 and 7 (itself) as those numbers.so, in simple sense, we can say that the prime number will only be divisible by itself and that will have no other factors will be called a prime number.
Types of Composite Numbers
There are primarily two types of composite numbers that we often come across
- Odd Composite Numbers or Composite Odd Numbers
- Even Composite Numbers or Composite Even Numbers
Odd Composite Numbers
All the odd integers that are not in the category of prime are odd composite numbers some of the examples of composite odd numbers are 9, 15, 21, 25, 27, 31, etc.
So, if we consider the numbers 1, 2, 3, 4, 9, 10, 11, 12, and 15. We can see that 9 and 15 are the odd composites as these two numbers have the odd divisors and so satisfy the composite condition.
Even Composite Numbers
If we take all the even integers which are not in the category of prime are even composite numbers. Few of the examples of composite odd numbers are 4, 6, 8, 10, 12, 14, 16, etc.
So, here 4, 10 and 12 are the even composites because these two numbers have the odd divisors and will satisfy the composite condition.