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Writing a number as a product of its prime factors
Factor ladders are an easy way to help you to do this. For example if you wanted to write 120 as a product of its prime factors you would start by dividing 120 by a nice small prime number like ‘2’.
|
2 |
120 |
|
|
60 |
120 divided by 2 is 60. 60 is not a prime number so we must find a prime number to divide 60 by, we can use 2 again.
|
2 |
120 |
|
2 |
60 |
|
|
30 |
Keep dividing by prime numbers until the number that is left is a prime number.
|
2 |
120 |
|
2 |
60 |
|
2 |
30 |
|
3 |
15 |
|
|
5 |
Looking at all the prime numbers that we have used, if we multiply them together we get back to 120.
2 x 2 x 2 x 3 x 5 = 120.
So 120 written as a product of its prime factors is 2 x 2 x 2 x 3 x 5.
We can also write this in index form 23 x 3 x 5.
Try writing these numbers as products of their prime factors and in index form:
|
1. 72 |
2. 150 |
3. 720 |
4. 80 |