Girl about Bath

Today with my class of 10 year olds, we continued discovering why maths is great.  Or rather, they continued humouring me while I got over-enthusiastic about numbers.  We found out that: 

• If you want to find out if a number is divisible by 3, you add together each of the digits in the number, and keep doing this until you have a single digit.  If that number is divisible by 3 (i.e. it’s 3, 6 or 9), the original number is too.

e.g. 45 4+5=9, so therefore 45 is divisible by 3.  

      1542 1+5+4+2=12   1+2=3, so therefore 1542 is divisible by 3.

This is just the beginning…

• If you want to find out if a number is divisible by 7, you take the last digit and double it, then subtract it from the rest of the number. If you get zero, or an answer divisible by 7, the original number is too.  If you don’t know the new number’s divisibility, you can apply the same principle again.

e.g. 203 : 3 doubled is 6, 20-6=14, so 203 is divisible by 7. 

7735 : 773-(5×2)=763, 76-(3×2)= 70 which is divisible by 7, so so is 7735.

• If you want to find out if a number is divisible by 11, alternately subtract then add the digits starting from left to right.  If the answer is zero or divisible by 11, so is the original number.

e.g. 365167484

3-6+5-1+6-7+4-8+4=0 so it is a multiple of 11.

914682538

9-1+4-6+8-2+5-3+8=22 so it is a multiple of 11. 

Oh the fun!  If you reached the end of this post, thanks for humouring me too.

NB: adding together the digits of a number finds that number’s ‘digital root’ (e.g. 12 = 1+2 = 3.)  If you get a multi-digit number when you do this, you keep adding the digits together until you reach a single digit answer.  Find the digital roots of the answers in all of the times tables and you’ll find loads of patterns!

Tags: divisibility, key stage 2, maths, multiple, primary school