Follow this recipe for sieving numbers and see what interesting patterns emerge.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
Can you work out what a ziffle is on the planet Zargon?
Given the products of adjacent cells, can you complete this Sudoku?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
A game that tests your understanding of remainders.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
56 406 is the product of two consecutive numbers. What are these
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Is there an efficient way to work out how many factors a large number has?
Got It game for an adult and child. How can you play so that you know you will always win?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Can you find any perfect numbers? Read this article to find out more...
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
Find the highest power of 11 that will divide into 1000! exactly.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.