Can you find a way to identify times tables after they have been shifted up?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
Is there an efficient way to work out how many factors a large number has?
A game that tests your understanding of remainders.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
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...
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
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
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Given the products of adjacent cells, can you complete this Sudoku?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Find the highest power of 11 that will divide into 1000! exactly.
Can you find any perfect numbers? Read this article to find out more...
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?
The nth term of a sequence is given by the formula n^3 + 11n . Find
the first four terms of the sequence given by this formula and the
first term of the sequence which is bigger than one million. . . .
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. . . .
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
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!?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
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?
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?"
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?