Factor Rules For Division And Multiplying

Factor Rules for Dividing Large Numbers

Being able to partition numbers and recognise when the best time to is essential in Maths, from simplifying fractions to real life situations like splitting a bill between friends or understanding finances and loans. Children are taught the easy methods like only dividing even numbers by 2, or recognising 5 & 10 timestables. But there are a range of patterns and methodologies to be aware of when it comes to dividing. To practice these rules we will be using 10,368 but you can use any number you like to experiment with the rules.


Factor Rules

3 - if you can add the digits of a number to make a multiple of 3, we can divide it by 3.

Take our example number 1236. 1 + 2 + 3 + 6 = 12, which is a multiple of 3. So we can confidently divide by 3 to get 412.

4 - if the last two digits of a number are in the 4 timestables we can divide by 4. This works because 4 will go into 100 25 times, meaning 4 will go into any number ending in `00`. If we start on round multiples of 4 like 20, 40, 60, 80 or 100 and +/- 4s, we can find a solution much quicker.

The last 2 digits of 1236 are 36 which is 4 x 9, so we know 4 will go into the whole number 309 times once divided.

6 - if a number has a factor both 3 and 2, it will have a factor of 6. All numbers have a factor of 1, so if a number is even and has a factor of 3 it will have all the factors of 6.

1236 already has 3 as a factor, and is even, so we can confidently divide by 6 to get 206.

9 - if a numbers digits adds up to 9 or 18 we can divide by 9.

The 9 timestables has a lot of tricks to it, but the best method to check for factors is if it`s digits add up to 9. This works with every number no matter how big, with only numbers like 11 x 9 = 99, 21x9 = 189, being numbers that add up to 18. Our number 10, 368 adds up to 18 making it a factor of 9.


12 and 24 - if a number has 4 and 6 as a factor it will have a factor of 12.

If we combine rules we can find even bigger numbers with factors. For example the factors of 12 are 1-12, 2-6 and 3-4. If a number has 6 as a factor it already has 2 and 3 as factors, so if that number also has 4 as a factor it`ll have all the factors of 12. Like wise, if a number has a factor of 12 (1, 2, 3, 4, 6) and 8 it`ll have all the factors of 24, and so on.

10368 has a factor of 1, 2, 3, 4, 6 and 8 so we can divide it by both 12 and 24.

25 if a number ends in 25, 50, 75 or 00 we can divide by 25. When dividing by 25 remember 25 is in 100 4 times, so if you`re dividing you can actually multiple the 100s by 4 and divide the tens by 25.

E.g. Our number can`t be divided by 25 but if we take 4575 then 4575 / 25 = 183 because our 100s column (45) x 4 = 180 and 75 / 25 = 3. This will be easier than dividing where you`ll have a lot of big remainders.

Understanding and applying these rules will help with confidence in simplifying fractions, and can assist in finding larger factor numbers and dividing into decimals.

Make sure that when you have figured out a number has a factor you still work out the answer no matter how sure you are on the answer!