What is the value of the digit A in the sum below: [3(230 + A)]^2 =
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?
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.
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
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 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 five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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?
Find the highest power of 11 that will divide into 1000! exactly.
56 406 is the product of two consecutive numbers. What are these
Number problems at primary level to work on with others.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Number problems at primary level that may require determination.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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 find?
Is there an efficient way to work out how many factors a large number has?
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?
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.
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Can you find any perfect numbers? Read this article to find out more...
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!?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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.
Have a go at balancing this equation. Can you find different ways of doing it?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Substitution and Transposition all in one! How fiendish can these codes get?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Given the products of adjacent cells, can you complete this Sudoku?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you work out what size grid you need to read our secret message?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
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?
Explore the relationship between simple linear functions and their
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. . . .
A game that tests your understanding of remainders.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?