Prime and composite numbers are differentiated based on the number of factors they have. These worksheets require students to identify prime or composite numbers, and they can use one of a collection prime or composite number charts to help!
Before we start with prime and composite numbers, let us first understand what factors are and how to find them.
There are two methods for finding factors:
Let’s try some examples.
Example 1: Find the factors of number 8.
Work from the outside in. Start dividing the number with the number itself then proceed with the next number that will divide it leaving no remainder.
8/8 = 1
8/4 = 2
8/2 = 4
8/1 = 8
Therefore, the factors of number 8 are 1, 2, 4, and 8.
These numbers are also called the divisors of 8. Factors of a number are also called divisors of that same number. The divisor of a number is the value that divides the number into exact parts, in other words, has a remainder of 0.
Another way of finding the factors of a number is through multiplication.
1x8 = 8
2x4 = 8
Here, the numbers that will give a product of 8 are the factors, which are also 1, 2, 4, and 8.
Example 2: Find the factors of 11.
11/1 = 11
11 is a prime number. It has only two factors, 1 and the number itself, which is 11.
Example 3: Find the factors of 36.
36/36 = 1
36/18 = 2
36/12 = 3
36/9 = 4
36/6 = 6
36/4 = 9
36/3 = 12
36/2 = 18
36/1 = 36
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
If we use multiplication, what numbers will give a product of 36?
1x36 = 36
2x18 = 36
3x12 = 36
4x9 = 36
6x6 = 36
We got the same factors ~ 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Take note that only positive numbers, whole numbers, and non-fractional numbers are considered when we are looking for factors.
Now that we already know what factors are and how to find them, we can easily distinguish the difference between prime and composite numbers. Read on…
Prime numbers are numbers that have only two factors, 1 and the number itself. For example, the smallest prime number is 2. It has only two factors, 1 and the number itself, which is 2. Any number that does not follow this is termed a composite number, which can be factored into other positive integers. Some other examples of prime numbers include 3, 5, 7, 11, 13, and so on.
Meanwhile, composite numbers are those numbers that have more than two factors. For example, the smallest composite number is 4. It has more than two factors. They are 1, 2, and 4. Numbers that are not prime are composite because they are divisible by more than two numbers. Other examples of composite numbers are 6, 8, 9, 10, and so on.
Also, we can say that except for 1, the remaining numbers are classified as prime and composite numbers. All prime numbers are odd numbers except 2, 2 is the smallest prime number and is the only even prime number.
So all whole numbers (except 0 and 1) are either prime or composite.
You may print this Prime and Composite Numbers Chart 1-100 to easily visualize what we discussed above. Other versions of charts are available too. You can choose to print from our 12 variations of charts in pdf format, including the Prime Numbers Chart and the Composite Numbers Chart, and a lot more.
0 and 1 are neither prime nor composite.
Any number multiplied by 0 will be equal to 0, which gives it more than 2 factors. So 0 is not a prime number. It is not a composite number either because all composite numbers have a finite number of factors, while 0 has an infinite number of factors.
1 is neither a prime number nor a composite number also because it has only 1 factor which is 1. Recall the definition of prime number, which states that a number should have exactly two factors, and composite number which states that a number should have more than 2 factors, number 1 has one and only one factor. Thus 1 is not considered a prime or a composite number. It is a unique number.