FACTORS AND MULTIPLES
1. FACTORS
A factor is a number that divides into another number exactly e.g., 2 ,4, and 8 are factors of 16; 2,3,4, and 6 are factors of 12.
When finding factors of a large number we use the “ladder method” and work with the prime numbers starting from the smallest e.g.,
2 5400
2 2700
2 1350
3 675
3 225
3 75
5 25
5
So the prime factors of 5400 are 23 x 33 x 52
This means that numbers such as any combinations of these prime numbers such as 6, 18, and 135 are also factors of 5400.
Factors are important when we work with fractions because they help us to simplify fractions e.g. 18/66 can be simplified when we see that 6 is a factor of 18 and of 66 so it can be simplified to 3/11.
2. MULTIPLES
A multiple of a number is what happens when we multiply that number by another number. Any two or more numbers can have common multiples e.g., 2,3 and 4 have common multiples of 12, 24 etc.
How to find the lowest common multiple
1. Do the other number divide exactly into the biggest number? Y – LCM; N – go to next step
2. Multiply the smallest two numbers and see if the other numbers divide into the result keep doing this with successively bigger numbers until you find the LCM e.g. 2,3, 5 – 2 x 3 = 6 not a common multiple; 2 X 5 = 10 not a CM; 3 X5 = 15 not a CM 2 x 3 x 5 = 30 – LCM!
Multiples are important with fractions because the lowest common denominator is actually a LCM of the denominators.