# Factors and Multiples

I want to share a few different activities that I use with pupils when working on factors and multiples.

• Finding the highest common factor. This is a problem solving activity I made to provide some extra challenge when finding the highest common factor. Working in small groups the pupils have to match a pair of numbers and a highest common factor. The trick is that there are different sets of numbers which will give the same highest common factor. I found that this tested the perseverance of my pupils.

This is a game for two players. The first player chooses a positive even number that is less than 50 and crosses it out on the grid. The second player chooses a number to cross out. The number must be a factor or multiple of the first number. Players continue to take it in turns to cross out numbers, at each stage choosing a number that is a factor or multiple of the number just crossed out by the other player.

The first person who is unable to cross out a number loses.

I make laminated sets of the game board so that they can easily be reused. It is interesting to see pupils figuring out a winning strategy the more they play.

It can be extended to have the two players working together to create the longest chain of numbers possible.

• Abundant Numbers (again taken from www.nrich.maths.org) I had heard of perfect numbers, where numbers are equal to the sum of all of their factors but not including the number itself. This little task involves pupils trying to find abundant numbers – which are numbers that are less than the sum of its factors (without itself). A nice task which can lead to questions such as why do you know that all prime numbers aren’t abundant numbers?

• Number Drop. This is a quick question that could be used as a starter or an exit ticket. It is based on an old exam question. There is an extension which allows pupils to create their own puzzle for others to solve.
All the resources for these activities can be found in my Resources page.