A game that tests your understanding of remainders.
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
A game in which players take it in turns to choose a number. Can you block your opponent?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides
exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest
power of two that divides exactly into 100!?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
In this activity, the computer chooses a times table and shifts it.
Can you work out the table and the shift each time?
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?
Given the products of diagonally opposite cells - can you complete
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
A number N is divisible by 10, 90, 98 and 882 but it is NOT
divisible by 50 or 270 or 686 or 1764. It is also known that N is a
factor of 9261000. What is N?
Can you find a way to identify times tables after they have been shifted up?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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. . . .
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
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 the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two
digit numbers are multiplied to give a four digit number, so that
the expression is correct. How many different solutions can you
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
What is the smallest number with exactly 14 divisors?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Can you find any perfect numbers? Read this article to find out more...
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?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Find the highest power of 11 that will divide into 1000! exactly.
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?