 # Prime Factors

 From: Anna Lahert Date: 19 March 1999 Subject: How to write a number as a product of prime factors I understand prime numbers and I understand factors. But I cannot understand Prime Factors - how do you know what numbers to choose?

### Maths Help suggests:

Writing a number as a product of its prime factors can be a useful way to analyse a number.

It can can be done 'freely', or in a more structured way.

## By Guesswork

Use your 'general knowledge' of tables to spot factors of the original number (except 1).
Repeat the process for each of these factors, until you can go no further.
This will happen when all of the factors are prime numbers.

 140 14 × 10 2 × 7 × 5 × 2
or...
 140 20 × 7 5 × 4 × 7 5 × 2 × 2 × 7
 So, writing the factors in numerical order: 140 = 2 × 2 × 5 × 7 or (even better): 140 = 22 × 5 × 7

Notice that it doesn't matter which factors of the original number you spot first.
You always end up with the same prime factorisation.

## Systematic Method

• Repeatedly divide out 2 as a factor until there are none left.
• Go to the next prime number, and repeatedly divide by 3.
• Continue in turn with the next prime numbers, until you are left with a prime number.

Example: Find the prime factorisation of 1386

 1386 ÷ 2 = 693 693 ÷ 2 2 is not a factor of 693. Try 3... 693 ÷ 3 = 231 231 ÷ 3 = 77 77 ÷ 3 3 is not a factor of 77. Try 5... 77 ÷ 5 5 is not a factor of 77. Try 7... 77 ÷ 7 = 11. Since 11 is prime, we can stop.

So: 1386 = 2 × 32 × 7 × 11

This is a better method to choose for larger numbers, or when it is hard to spot factors.