What are Composite Numbers?

Composite numbers are positive integers that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or unit 1, so the composite number is exactly the numbers that are not prime and not a unit.

Ex: The integer 14 is a composite number because it is the product of the two smaller integers 2 × 7. Likewise, the integers 2 and 3 is not a composite number because each of them can only be divided by one and itself.

Determine the Composite Numbers?

The procedures to find whether a given number is prime or composite:

  • Find all the factors of the positive integer
  • A number is said to be prime if it has only two factors, 1 and itself.
  • If the number has more than two factors, then it is a composite.

Example: Find if 16 is a composite number.

Let us find the factors of 16.

  • 16 x 1 = 16
  • 8 x 2 = 16
  • 16 x 1 = 16
  • 4 x 4 = 16

As we can see, the factors of 16 are 1,2, 4and 8 so it is a composite number.

Composite Numbers

Types of Composite Numbers

There are 2 main types of composite number in Maths which are:

  1. Odd Composite Number: All the odd integers which Are not prime are an odd composite number. Examples of composite odd numbers are 9, 15, 21, 25, 27, 31, etc. Consider the numbers 1, 2, 3, 4, 9, 10, 11,12, and 15 . Here 9 and 15 are the odd composites because those two numbers have the odd divisors and satisfy the composite condition.
  2. Even Composite Number: All the even integers which are not prime are even composite numbers. Examples of composite odd numbers are 4, 6, 8, 10, 12, 14, 16, etc. Consider the numbers 1, 2, 3, 4, 9, 10, 11,12, and 15 again . Here 4, 10, and 12 are the even composites because those two numbers have the odd divisors and satisfy the composite condition.

Composite numbers up to 150

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. (sequence A002808 in the OEIS)

Every composite number can be written as the product of two or more (not necessarily distinct) primes. For example, the composite number 299 can be written as 13 × 23, and the composite number 360 can be written as 23 × 32 × 5; furthermore, this representation is unique up to the order of the factors.

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