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## Prime Factorisation

Any natural number greater than 1 can be represented in exactly one way as a product of primes. This theorem is called the Fundamental Theorem of Arithmetic.

Here is a good way to find the prime factorization of a small number:

1. If the number is not prime, find a small prime number that divides exactly into the given number.
2. Divide the number by the prime to obtain a quotient.
3. Repeat the process with the quotient until the quotient is itself a prime number.
4. The prime factorization is given by the product of the primes used in the division process and the final prime quotient.

Fortunately there are some simple rules to find out whether the number is divisible by a small prime.

1. If the number ends in 2,4,6,8 or 0 it is divisible by 2.
2. If the digits of the number add to a number that is divisible by 3, then the original number is also divisible by 3.
3. If the number ends in 5 or 0, it is divisible by 5.

### Example

Find the prime factorization of 462: If p is a prime we will call pn a prime power.

### Exercise

Factorise the number then check your answer.

 Number Factorization

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