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

 

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.


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