Optimus Prime

Prime factors have nothing to do with Optimus Prime – sadly – but they often crop up in Maths tests and can be used to find the Lowest Common Multiple or Highest Common Factor of two numbers.

Prime factors are the lowest prime numbers that can be multiplied together to make a given number. There are two methods of finding out what they are: the ladder method and the factor tree. I prefer the ladder method.

**Ladder method**

- Write down the number for which you want to find the prime factors.
- Find the lowest prime number that goes into it exactly and write it down next to it on the same line.
- Divide one number by the other and write down the result under the original number on the next line.
- Repeat steps 2 and 3 until you reach the number 1.
- Draw a line between the two columns and lines after the first row and before the last.
- Write down the prime factors from the column you have just created, using powers to simplify the expression, eg the factors of 12 are 2² x 3, not 2 x 2 x 3.

**Lowest Common Multiple (LCM)**

Prime factors are useful in working out the Lowest Common Multiple (LCM) of two numbers, in other words the lowest number that is divisible by both numbers.

- Work out the prime factors of the two numbers and write them down one below the other, eg the prime factors of 30 are 2 x 3 x 5, and the prime factors of 45 are 3 x 3 x 5.
- Make a new list by writing down each factor the greatest number of times it appears in either list, eg there are two 3s in one list and one in the other, so the new list is 2 x 3 x 3 x 5.
- Multiply together the new list of factors, eg the LCM of 30 and 45 is 2 x 3 x 3 x 5 = 90.

**Highest Common Factor (HCF)**

Prime factors can be used to work out the Highest Common Factor (HCF) of two numbers, in other words the highest number that both numbers can be divided by exactly.

- Work out the prime factors of the two numbers and write them down one below the other, eg the prime factors of 30 are 2 x 3 x 5, and the prime factors of 45 are 3 x 3 x 5.
- Make a new list by writing down each factor that appears in both lists, eg 3 and 5 appear in both lists, so the new list is 3 x 5.
- Multiply together the new list of factors, eg the HCF of 30 and 45 is 3 x 5 = 15.

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