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Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
Can you work out what size grid you need to read our secret message?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Have you seen this way of doing multiplication ?
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.
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 hit?
Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
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. . . .
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Can you find a way to identify times tables after they have been shifted up?
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 can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find the highest power of 11 that will divide into 1000! exactly.
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
A collection of resources to support work on Factors and Multiples at Secondary level.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Given the products of adjacent cells, can you complete this Sudoku?
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
Substitution and Transposition all in one! How fiendish can these codes get?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
A game in which players take it in turns to choose a number. Can you block your opponent?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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. . . .
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
Can you find what the last two digits of the number $4^{1999}$ are?
A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?
Explore the relationship between simple linear functions and their graphs.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
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?
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...
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. . . .
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?
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.
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?
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.