Composite Numbers
Nov 30, 2022, 16:45 IST
Composite numbers are that numbers which is more than two factors. These numbers are also called composites. It is the exact opposite of prime numbers, with only two factors, i.e., 1 and the number itself. All non-prime natural numbers are composite numbers because they are divisible by more than two numbers. For e.g., 8 is a composite number because it is divisible by 1, 2, 4, and an even number of 8.
In this article, we go through the definition of composite numbers, properties, smallest composite numbers, even and odd composite numbers, a list of composite numbers, and the difference between prime numbers and composite numbers.
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What is Composite Number?
A number divisible by a number other than 1 and the number itself is called a composite number. For example, 6 is a number divisible by 1, 2, and 3, so it is a composite number.
Composite Number Definition
In mathematics, a natural number which has more than two factors is known as a Composite number. Let us know more about the composite numbers with examples.
Composite Numbers Examples
The few composite numbers are 4, 6, 8, 9, and 10. Let us take 4 and 10. In the above example, 4 and 10 are called composite numbers because they have more than 2 factors. Now, let us understand the important properties of composite numbers.
How to Find Composite Numbers?
To find a composite number, we have to find the factors of the given number. If a number has more than two factors, it is composite. The best way to find out a composite number is to do a divisibility test. The divisibility test helps us determine whether a number is prime or composite. Divisibility means that a number is completely (without a remainder) divided by another number other than 1.
To do this, we need to check if the number is divisible by these common factors: 2, 3, 5, 7, 11, and 13. If the number is even, then start checking with 2. If the number ends with 0 or 5, then check by 5. If the number cannot be divided by any of these given numbers, then the number is prime. For example, 36 is divisible by 2, which means it has factors other than 1 and 13, so we can say that 36 is a composite number.
Properties of Composite Numbers
- Composite numbers have more than two factors
- Composite numbers are divisible by their factors
- Each composite number is a factor in itself
- The smallest composite number is 4
- Every composite number will include at least two primes as its factors (eg 35 = 5 x 7, where 5 and 7 are primes)
- Composite numbers are also divisible by other composite numbers
Types of Composite Numbers
There are two types of Composite number:
- Odd Composite Number
- Even Composite Number
Odd Composite Number
All odd integers that are not prime are known as a composite odd number. For example, odd composite numbers are 9, 15, 21, 25, and 27. Consider the numbers 1, 2, 3, 4, 9, 10, 11, 12 and 15. Here 9 and 15 are odd composite numbers because these two odd numbers have more than 2 factors and satisfy the composite number condition.
Even Composite Number
All non-prime even numbers are known as composite even numbers. For example, 4, 6, 8, 10, 12, 14, and 16 are even composite numbers. Consider again the numbers 1, 2, 3, 4, 9, 10, 11, 12, and 15. Here, 4, 10, and 12 are even composite numbers because these even numbers have more than 2 factors and satisfy the composite number condition.
Smallest Composite Number
The smallest composite number is 4. A composite number is a number with divisors other than 1 and the number itself. Now, if we start counting: 1, 2, 3, 4, 5, 6, .... and so on, as we know that 1 is also not a composite number because it has one divisor i.e, 1. 2 is also not a composite number because it has only two divisors, i.e., 1 and 2 itself. 3 is also not a composite number because it has only two divisors, i.e., 1 and 3 itself. However, when we come to the number 4, we know that its divisors are 1, 2, and 4. So the number 4 meets the criteria of a composite number. Therefore, 4 is the smallest composite number.
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Difference Between Prime and Composite Numbers
| Prime Numbers | Composite Numbers |
| It can only be divided by 1 and itself, thus have only two factors. | It has more than two factors (1 and itself). |
| It can only be written as a product of two numbers | It can be written as the product of two or more numbers |
| Example: 5 has factors are 1 and 5 | Example: 4 has factors are 1, 2 and 4 |
Solved Examples
Q1. Find 328 is a composite number.
Ans. 1, 2, 4, 8, 41, 82, 164, 328 are the factor of 328. Therefore, 328 is a composite number.
Q2. What is the prime factorization of 60?
Ans. The prime factorization of 60 is:
60 = 2 × 2 × 3 × 5.
Q3. List out all the composite numbers from the set of numbers given below.
2, 4, 9, 11, 21, 31, 44, 53, 67, 88, 101, 108
Ans. The composite numbers is 4, 9, 21, 44, 88, and 108.
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Frequently Asked Questions (FAQs)
Q1. What is the rule for composite numbers?
Ans. Find all the number factors to determine whether a number is composite or prime. If a number has only two factors, 1 and itself, it is prime. If a integer has more than two factors, it is composite.
Q2. How are composite numbers formed?
Ans. A composite number is a positive number that is formed by multiplying two smaller positive integers. Equivalently, it is a positive integer with at least one divisor other than 1.
Q3. Do composite numbers have factors?
Ans. Composite numbers are numbers which has more than two factors. These numbers are also called composites. It is the exact opposite of prime numbers, with only two factors, i.e., 1 and the number itself.
Q4. Is 0 composite or prime?
Ans. 0 is neither prime nor composite. Since any number of times, zero equals zero, there are an infinite number of factors for the product of zero. A composite number must have a factor of finite numbers. One is also neither prime nor composite.
