Factors and multiples

There are 252 NRICH Mathematical resources connected to Factors and multiples
Grouping Goodies
problem
Favourite

Grouping goodies

Age
5 to 7
Challenge level
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Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Neighbours
problem
Favourite

Neighbours

Age
7 to 11
Challenge level
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In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Lots of Lollies
problem
Favourite

Lots of lollies

Age
5 to 7
Challenge level
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Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Domino Pick
problem
Favourite

Domino pick

Age
5 to 7
Challenge level
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Are these domino games fair? Can you explain why or why not?
I Like ...
problem
Favourite

I like ...

Age
5 to 7
Challenge level
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Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Curious number
problem
Favourite

Curious number

Age
7 to 11
Challenge level
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Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Fac-Finding
problem
Favourite

Fac-finding

Age
14 to 16
Challenge level
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Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
Same Length Trains
problem
Favourite

Same length trains

Age
5 to 7
Challenge level
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How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
Clapping Times
problem
Favourite

Clapping times

Age
5 to 7
Challenge level
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If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
Counting Cogs
problem
Favourite

Counting cogs

Age
7 to 14
Challenge level
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Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?