# Check whether a number is prime, composite numbers prime factorization (prime decomposition) as products of factors in exponential form

## Latest factored numbers

 4,602 = 2 × 3 × 13 × 59 Jan 22 14:57 UTC (GMT) 4,259,455 = 5 × 851891 Jan 22 14:57 UTC (GMT) 255 = 3 × 5 × 17 Jan 22 14:57 UTC (GMT) 207,899,997 = 3 × 69299999 Jan 22 14:56 UTC (GMT) 400 = 24 × 52 Jan 22 14:56 UTC (GMT) 110 = 2 × 5 × 11 Jan 22 14:56 UTC (GMT) 99 = 32 × 11 Jan 22 14:56 UTC (GMT) 165 = 3 × 5 × 11 Jan 22 14:56 UTC (GMT) 1,320 = 23 × 3 × 5 × 11 Jan 22 14:56 UTC (GMT) 100 = 22 × 52 Jan 22 14:56 UTC (GMT) 789,654,123,654 = 2 × 3 × 11 × 37 × 323363687 Jan 22 14:56 UTC (GMT) 38,023 = 47 × 809 Jan 22 14:56 UTC (GMT) 105 = 3 × 5 × 7 Jan 22 14:56 UTC (GMT) see more... integer numbers factored, broken down to prime factors

## Prime numbers definition. Composite numbers

#### A composite number is a positive integer that has at least one positive 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.

• 2 is divisible only by 2 and 1, so 2 is a prime number
• 3 is divisible only by 3 and 1, so 3 is a prime number
• 5 is divisible only by 5 and 1, so 5 is a prime number
• 13 is divisible only by 13 and 1, so 13 is a prime number

#### 1 is not considered prime, so the first prime number is 2 (prime numbers list is starting with the number 2)

##### 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. Prime numbers are thus the basic building blocks of all numbers. If 1 were admitted as a prime, number 15 for example could be factored as 3 × 5 and 1 × 3 × 5; these two representations would be considered different prime factorizations of 15 (prime factorization into prime factors), so the statement of the theorem would have to be modified.
• 4 is divisible by 4, 2 and 1, so 4 is not a prime number, it's a composite number; 4 = 22
• 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime number, it's a composite number; 6 = 2 × 3
• 8 is divisible by 8, 4, 2 and 1, so 8 is not a prime number, it's a composite number; 8 = 23
• 9 is divisible by 9, 3, and 1, so 9 is not a prime number, it's a composite number; 9 = 32

Examples of prime numbers, 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