# Is the integer 1 a prime or a composite number?

## Latest factored numbers

 1 is considered neither a prime nor a composite number May 21 05:23 UTC (GMT) 5,678,999 = 23 × 246913 May 21 05:23 UTC (GMT) 400 = 24 × 52 May 21 05:23 UTC (GMT) 162 = 2 × 34 May 21 05:23 UTC (GMT) 54 = 2 × 33 May 21 05:23 UTC (GMT) 406 = 2 × 7 × 29 May 21 05:22 UTC (GMT) 111 = 3 × 37 May 21 05:22 UTC (GMT) 347 is a prime number, it cannot be prime factorized into other prime factors May 21 05:22 UTC (GMT) 23,777,774 = 2 × 89 × 133583 May 21 05:22 UTC (GMT) 268 = 22 × 67 May 21 05:22 UTC (GMT) 401,210 = 2 × 5 × 53 × 757 May 21 05:22 UTC (GMT) 23,777,774 = 2 × 89 × 133583 May 21 05:22 UTC (GMT) 528 = 24 × 3 × 11 May 21 05:21 UTC (GMT) see more... integer numbers factored down to their prime factors

## Tutoring: composite numbers prime factorization (decomposing, breaking numbers down to their prime factors)

The fundamental theorem of arithmetic says that every integer larger than 1 can be written as a product of one or more prime numbers in a way that is unique, except for the order of the prime factors.

1 is not considered prime, so the first prime number is 2. If 1 were admitted as a prime, number 15 for example could be prime factorized as 3 × 5 and 1 × 3 × 5; these two representations would be considered different prime factorizations, so the theorem above would have to be modified.

Positive integers that are only dividing by themselves and by number 1 are called prime numbers. If a number is prime, it can not be factored down to other prime factors, it is divisible only by 1 and itself; the number itself is called an IMPROPER FACTOR (improper divisor). Some people also consider 1 as an improper factor.

A composite number is a positive integer that has at least one positive factor (divisor) other than 1 and the number itself. A composite number is also any positive integer larger than 1 that is not a prime number.

A prime number can't be factored down to prime factors, but a number that is a composite can be, as it is shown bellow:

Example 1: 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime, it's a composite number; 6 can be factored in different ways, as 1 × 6, or 1 × 2 × 3, or 2 × 3; but its prime factorization is always: 6 = 2 × 3.

Example 2: 120 can be factored in different ways, as 4 × 30 or 2 × 2 × 2 × 15 or 2 × 2 × 2 × 3 × 5; its prime factorization is always: 120 = 23 × 3 × 5; this is the condensed form of writing, with exponents, of the longer: 120 = 2 × 2 × 2 × 3 × 5.

It is important to know about numbers prime factorization in order to calculate the greatest common factor GCF of numbers (also called the greatest common divizor GCD, or highest common factor, HCF) - GCF is needed when reducing (simplifying) fractions to the lowest terms, or to calculate the least common multiple, LCM - this is needed when adding or subtracting ordinary fractions...

Example of prime numbers: 2 is divisible only by 2 and 1, so 2 is a prime number; 13 is divisible only by 13 and 1, so 13 is a prime number;

Please have a look at all the prime numbers, from 2 up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Prime numbers are used as basic blocks when building the prime factorizations of the composite numbers.