A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number.
So, if n > 0 is an integer and there are integers 1 < a, b < n such that n = a × b, then n is composite. By definition, every integer greater than one is either a prime number or a composite number. The number one is a unit – it is neither prime nor composite. For example, the integer 14 is a composite number because it can be factored as 2 × 7. Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself.
The first 105 composite numbers (sequence A002808 in OEIS) are
- 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.
Every composite number can be written as the product of two or more (not necessarily distinct) primes; furthermore, this representation is unique up to the order of the factors. This is called the fundamental theorem of arithmetic.
There are several known primality tests that can determine whether a number is prime or composite, without necessarily revealing the factorization of a composite input.
Read more about Composite Number: Types of Composite Numbers
Famous quotes containing the words composite and/or number:
“A positive learning climate in a school for young children is a composite of many things. It is an attitude that respects children. It is a place where children receive guidance and encouragement from the responsible adults around them. It is an environment where children can experiment and try out new ideas without fear of failure. It is an atmosphere that builds children’s self-confidence so they dare to take risks. It is an environment that nurtures a love of learning.”
—Carol B. Hillman (20th century)
“Ah, but to play man number one,
To drive the dagger in his heart,
To lay his brain upon the board
And pick the acrid colors out,
To nail his thought across the door,
Its wings spread wide to rain and snow,
To strike his living hi and ho....”
—Wallace Stevens (1879–1955)