Numbers with more than two factors are called composite numbers, and since natural numbers go all the way to infinity, there are a lot of them. In the modern world, composite numbers are used to encrypt sensitive information in computer languages, and not a day on earth goes by without them being used.
What are composite numbers in math?
A composite number is a positive integer n>1 that has factors other than 1 and itself, unlike prime numbers. In other words, composite numbers are divisible by at least 3 positive integers. All whole numbers that are not prime numbers are composite numbers, except for 1.
Composite numbers examples
The first few consecutive composite numbers are 4, 6, 8, 9, and 10. Let’s consider 9 and 12 for our example:
The positive integer 9 is an odd composite number because it has more than 2 factors and it is not divisible by 2.
9⇶ 1, 3, 9
The positive integer 12 is a composite number since it has more than 2 factors.
1, 2, 3 ⇚12⇛ 4, 6, 12
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Properties of composite numbers
The properties of composite numbers are not too complicated:
- Composite numbers have more than two factors
- They are evenly divisible by their factors
- The smallest composite number is 4
- Composite numbers will include at least two prime numbers as their factors
List of composite numbers
Here is a list of composite numbers from 1 to 100:
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, 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, 93, 94, 95, 96, 98, 99.
Odd composite numbers
All the odd integers that aren’t prime are referred to as odd composite numbers. From 1 to 100, there are a total of 25 odd composite numbers: 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, and 99 are among the odd composite numbers from 1 to 100.
Composite numbers 1 to 200
This is for the curious among you who would like to know the composite numbers after 100. You can rest assured that no teacher will ever force you to learn them by heart:
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, 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, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 164, 165, 166, 168, 169, 170, 171, 172, 174, 175, 176, 177, 178, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 194, 195, 196, 198, 200.
How to find a composite number
To find a composite number, you must first determine the factors of the given integer. The number is composite if it has more than two elements. The divisibility test is the best approach to figure out a composite number. A number can be divided entirely (with no residue) by another number if it is divisible.
To do so, see if the number can be split by any of the following common factors: 2, 3, 5, 7, 11, and 13. Start verifying with the number 2 if the given number is even. If the number has a 0 or a 5, multiply it by 5. A prime number cannot be split by any of the other numbers than by one and itself. For instance, 68 is divisible by 2, indicating that it has factors other than 1 and 68, meaning that it is a composite number.
Types of composite numbers
Odd composite numbers and even composite numbers are the two types of composite numbers in math. Let’s take a look at each of them separately:
Odd Composite Numbers
Odd composite numbers are all odd numbers that aren’t prime. Odd composite numbers include 9, 15, 21, 25, and 27. Consider the numbers 9 and 15. Because these two numbers have odd divisors and satisfy the composite number criterion, 9 and 15 are odd composites.
Even Composite Numbers
Even composite numbers are all even numbers that aren’t prime. 4, 6, 8, 10, 12, 14, and 16, for example, are even composite numbers. They are even composites because they have more than two factors and are even.
Smallest composite number
The smallest composite number is 4. Because 1 has just one divisor, it is not a composite or prime number. The positive integers 2 and 3 are prime numbers because they can only be divided by one and themselves. As a result, 2 and 3 aren’t composite.
Important points to keep in mind when using composite numbers:
- 4 is the smallest composite number.
- 2 is the smallest prime number.
- 9 is the smallest odd composite number.
- 10 is the smallest two-digit composite number.
Difference between prime and composite numbers
A composite number has more than two factors, whereas a prime number has exactly two. For example, the number 5 can only be factored by 5 and 1. As a result, the number 5 is a prime number. Now, consider the number 8, which has multiple factors: 1, 2, 4, and 8. As a result, 8 isn’t a prime number.
Examples of Composite Numbers
H3: Determine whether 57 appears in the list of composite numbers from 1 to 100. What are its factors?
The number 57 is a composite number because it can be divided by more than two numbers. 1, 3, 19, and 57 are the factors of 57.
Determine whether the number 81 is a composite number.
The number given is 81. 1, 3, 9, 27, and 81 are all factors of 81. It’s a composite number because it has more than two factors. You can also use the composite numbers 1 to 100 chart to double-check your result.
Is 299 a composite or prime number?
To begin, you must determine whether 299 is divisible by 2. Because 299 is an odd number, we know it isn’t divisible by two. The next step is to determine whether 299 is divisible by three… it is not.
Then, you have to determine whether 299 is divisible by 5. We know 299 isn’t divisible by 5 without doing a sum because it doesn’t end in either a 5 or a 0. We must now determine if 299 is divisible by 7. A quick calculation reveals that 299 is not divisible by 7.
This is a more difficult example because 299 is a large number. This is a fantastic opportunity to put your division abilities to the test. If you keep dividing 299 by various numbers, you’ll discover that it may be split into 13 and 23. This means it’s an odd composite number!
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