Composite number
A composite number is a positive integer that can be formed by multiplying together 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 the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit.
For example, 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 are not composite numbers because each of them can only be divided by one and itself.
The composite numbers up to 150 are
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. This fact 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.
One way to classify composite numbers is by counting the number of prime factors. A composite number with two prime factors is a semiprime or 2-almost prime (the factors need not be distinct, hence squares of primes are included). A composite number with three distinct prime factors is a sphenic number. In some applications, it is necessary to differentiate between composite numbers with an odd number of distinct prime factors and those with an even number of distinct prime factors. For the latter
(where μ is the Möbius function and x is half the total of prime factors), while for the former
However, for prime numbers, the function also returns −1 and . For a number n with one or more repeated prime factors,
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