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

## Latest factored numbers

 134,996 = 22 × 33749 Jun 02 12:19 UTC (GMT) 1,506 = 2 × 3 × 251 Jun 02 12:19 UTC (GMT) 11,368,813 = 43 × 264391 Jun 02 12:19 UTC (GMT) 48,564 = 22 × 32 × 19 × 71 Jun 02 12:19 UTC (GMT) 343 = 73 Jun 02 12:19 UTC (GMT) 1,957,072 = 24 × 13 × 972 Jun 02 12:19 UTC (GMT) 67,581 = 33 × 2503 Jun 02 12:19 UTC (GMT) 1,362,821 = 37 × 36833 Jun 02 12:19 UTC (GMT) 50,777,775 = 32 × 52 × 127 × 1777 Jun 02 12:19 UTC (GMT) 12,936 = 23 × 3 × 72 × 11 Jun 02 12:19 UTC (GMT) 144 = 24 × 32 Jun 02 12:19 UTC (GMT) 51,872 = 25 × 1621 Jun 02 12:19 UTC (GMT) 1,103 is a prime number, it cannot be broken down to other prime factors Jun 02 12:18 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