What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Take any pair of numbers, say 9 and 14. Take the larger number,
fourteen, and count up in 14s. Then divide each of those values by
the 9, and look at the remainders.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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. . . .
Have you seen this way of doing multiplication ?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
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. . . .
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?
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...
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?
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.
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Given the products of adjacent cells, can you complete this Sudoku?
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?
What is the smallest number with exactly 14 divisors?
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?
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?"
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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.
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?
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.
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?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Each letter represents a different positive digit
AHHAAH / JOKE = HA
What are the values of each of the letters?
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.
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?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Substitution and Transposition all in one! How fiendish can these codes get?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Find the highest power of 11 that will divide into 1000! exactly.
Can you work out what size grid you need to read our secret message?
Can you find any perfect numbers? Read this article to find out more...
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
A game that tests your understanding of remainders.
Can you find a way to identify times tables after they have been shifted up?
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. . . .
Data is sent in chunks of two different sizes - a yellow chunk has
5 characters and a blue chunk has 9 characters. A data slot of size
31 cannot be exactly filled with a combination of yellow and. . . .