About: GMAT, MBA, Prime Number Factorisation, Quantitative
Ok, this is a tough one and took me a couple of days to get used to this but once you practice a few times you will get it.
Prime factorisation is basically finding the number of factors that make up any number. The GMAT will often asks questions about the highest common factor of two numbers or the lowest common multiple. This is what prime factorisation will do for you.
So, the first thing to do is work out how many factors go into any number, lets pick three random numbers to do this.
Lets say we pick 180. How many factors does 180 have? To find out we break down 180 to smallest prime number we can find (meaning it is no longer divisible).
180 = 2 x 90 2 is the lowest prime number so we will keep that one and try to break down the 90 further.
180 = 2 x 2 x 45 2 again is the lowest prime number but we can still break down the 45.
180 = 2×2 x 5 x 9 5 is a prime number so can’t be broken down further, 9 is not a prime number
180 = 2 x 2 x 5 x 3 x 3 now that we have all prime numbers we can tidy it up a little.
180 = 2² x 5 x 3² excellent, now time to find out the number of factors in 180. For each number we have we need to just take the exponent of each number and add 1 to it. 5 is of course 5¹. This means that we end up with:
3 x 2 x 3 = 18 There are 18 factors in 180. We can now put this to good practice and check it out:
Factors of 180
(1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180)
There are indeed 18 numbers and thus our prediction that there would be 18 factors is correct.
About: GMAT, MBA, Prime Number Factorisation, Quantitative
