# Composite numbers prime factorization (prime decomposition) as a product of factors in exponential form, by the calculator.

## Latest factored numbers

 37,948,222 = 2 × 13 × 61 × 71 × 337 Jan 21 20:58 UTC (GMT) 341,142 = 2 × 3 × 56857 Jan 21 20:58 UTC (GMT) 100 = 22 × 52 Jan 21 20:58 UTC (GMT) 936 = 23 × 32 × 13 Jan 21 20:58 UTC (GMT) 144,401 = 197 × 733 Jan 21 20:58 UTC (GMT) 11,664 = 24 × 36 Jan 21 20:58 UTC (GMT) 729 = 36 Jan 21 20:58 UTC (GMT) 72,728,283 = 3 × 311 × 77951 Jan 21 20:58 UTC (GMT) 92,742 = 2 × 3 × 13 × 29 × 41 Jan 21 20:58 UTC (GMT) 831,109 is a prime number, it cannot be broken down to other prime factors Jan 21 20:58 UTC (GMT) 965 = 5 × 193 Jan 21 20:58 UTC (GMT) 80,324 = 22 × 43 × 467 Jan 21 20:58 UTC (GMT) 7,777,777,770 = 2 × 32 × 5 × 7 × 37 × 333667 Jan 21 20:58 UTC (GMT) see more... integer numbers factored, broken down to 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.