## Prime Numbers and Prime Factorization

*See also: numbers, GCD and LCM*

**Prime numbers** are positive integers that have exactly 2 factors, that is 1 and itself. For example, 7 is a prime number because its only factors are 1 and 7.

#### Do you know?

The largest known prime number to date is 2^{77,232,917} − 1.

It was found on 26 December 2017 and has 23,249,425 digits. It is also the 50th known Mersenne Prime.

The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, and so on. Please note that 1 is not prime because it only has one factor.

You can check whether a number is a prime or not by entering the number below. If the only prime factor of that number is itself, then it's a prime number.

**Prime factors** are factors of an integer that are prime. Prime factors can be used to find Highest Common Factor and Lowest Common Multiple of two or more integers.

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### How to find prime factors of a number?

To find the prime factors of a number we can repeatedly divide by prime numbers.

For example to find the prime factors of 36, we would do the folowing steps.

- Divide 36 by the smallest prime number, that is, divide 36 by 2

36 ÷**2**= 18 - Now since 18 is divisible by 2, divide 18 by 2

18 ÷**2**= 9 - 9 is not divisible by 2, so try to divide it by the next prime number, that is 3

9 ÷**3**=**3** - 3 is a prime number, so we can stop here. And the prime factors are the ones that we have used in the divisions above including the last prime number that we got as a result of the division(the ones in bold)

So, 36 = 2 × 2 × 3 × 3

Or in index notation: 36 = 2^{2}× 3^{2}

Another example to find the prime factors of 42.

- 42 ÷
**2**= 21

21 ÷**3**=**7** - So, 42 = 2 × 3 × 7

*See also: numbers, GCD and LCM*