What Are Composite Numbers?

What are composite numbers? What’s the difference between composite numbers and prime numbers? If you’re looking to learn more about how to classify numbers, you’ve come to the right place. Here are some of the answers to the common questions that people have about composite numbers.

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What Are Composite Numbers?

Composite numbers are whole numbers that have at least three factors. Prime numbers have two factors: one and itself. For example, the only factors for 2 is 1 and 2 (1 x 2). However, 4 has 3 factors: 1, 2, and 4 (1 x 4 and 2 x 2). When you want to determine whether a number is prime or composite, you must figure out how many factors that number has.

Which Numbers Are Composite?

From 1 to 100, the following are composite numbers:
4, 6, 8, 9, 10
12, 14, 15, 16, 18, 20
21, 22, 24, 25, 26, 27, 28, 30
32, 33, 34, 35, 36, 38, 39, 40
42, 44, 45, 46, 48, 49, 50
51, 52, 54, 55, 56, 57, 58, 59, 60
62, 63, 64, 65, 66, 68, 69, 70
72, 74, 75, 76, 77, 78, 80
81, 82, 84, 85, 86, 87, 88, 90
91, 92, 94, 95, 96, 98, 99, 100

How Can You Test for Composite Numbers?

The best way to figure out if it’s a composite number is to perform the divisibility test. To do this, you should check to see if the number can be divided by these common factors: 2, 3, 5, 7, 11, and 13. If the number is even, then start with the number 2. If the number ends with a 0 or 5, try dividing by 5. If the number can’t be divided by any of these 6 numbers, then the number is most likely a prime number.

Test your skills with the divisibility test with the following 4 examples:

243

Since the number ends with a 3, we know that it isn’t an even number. Therefore, it’s not divisible by 2. Also, it doesn’t end with a 0 or 5, so it isn’t divisible by 5 either. So, we can move onto the next lowest number: 3.
243/3 = 81

Since the number has more than 2 factors, we know that it’s a composite number. The factors of 243 are 1, 3, 8, 27, 81, 243 (1 x 243, 3 x 81, 9 x 27).

283

As we perform the divisibility test with 283, we find that
283/2 = 141.5
283/3 = 94.33
283/5 = 56.6
283/7 = 40.43
283/11 = 25.72
283/13 = 21.76

Since none of the quotients are whole numbers, we can confidently say that 283 is a prime number.

187

We can weed out 2 and 5 as factors for 187. Then, we move onto the rest of the numbers. We end up with the following quotients:
187/3 = 62.33
187/7 = 26.71

Then, we get to 11 and find 187/11 = 17. The factors of 187 are 1, 11, 17, and 187, so it’s a composite number.

113

Once again, the number is odd and doesn’t end with 0 or 5. We can try to multiply it by 3, 7, 11, and 13, but we end up with a remainder or a decimal point. Since there are no other whole number factors, the only factors are 1 and 113, making it a prime number.

So, what are composite numbers? Composite numbers are whole numbers that have at least three factors. Performing the divisibility test will help you determine whether or not a number is a prime or composite number.

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