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Broad Topics > Numbers and the Number System > Factors and multiples ### Graphing Number Patterns

##### Age 7 to 11 Challenge Level:

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too? ### Three Spinners

##### Age 7 to 11 Challenge Level:

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner? ### What Do You Need?

##### Age 7 to 11 Challenge Level:

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? ### Which Is Quicker?

##### Age 7 to 11 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why? ### Path to the Stars

##### Age 7 to 11 Challenge Level:

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off? ### In the Money

##### Age 7 to 11 Challenge Level:

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there? ### What's in the Box?

##### Age 7 to 11 Challenge Level:

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box? ### Flashing Lights

##### Age 7 to 11 Challenge Level:

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? ### Tom's Number

##### Age 7 to 11 Challenge Level:

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'. ### Red Balloons, Blue Balloons

##### Age 7 to 11 Challenge Level:

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst? ### Spelling Circle

##### Age 7 to 11 Challenge Level:

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn. ### Ducking and Dividing

##### Age 7 to 11 Challenge Level:

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive? ### Factor-multiple Chains

##### Age 7 to 11 Challenge Level:

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers? ### Divide it Out

##### Age 7 to 11 Challenge Level:

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10? ### Multiplication Series: Number Arrays

##### Age 5 to 11

This article for teachers describes how number arrays can be a useful reprentation for many number concepts. ### Money Measure

##### Age 7 to 11 Challenge Level:

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes? ### What Two ...?

##### Age 7 to 11 Short Challenge Level:

56 406 is the product of two consecutive numbers. What are these two numbers? ### Crossings

##### Age 7 to 11 Challenge Level:

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest? ### Table Patterns Go Wild!

##### Age 7 to 11 Challenge Level:

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids. ### Which Numbers? (1)

##### Age 7 to 11 Challenge Level:

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues? ### Which Numbers? (2)

##### Age 7 to 11 Challenge Level:

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues? ### Becky's Number Plumber

##### Age 7 to 11 Challenge Level:

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? ### Three Neighbours

##### Age 7 to 11 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice? ### Give Me Four Clues

##### Age 7 to 11 Challenge Level:

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? ### Gabriel's Problem

##### Age 11 to 14 Challenge Level:

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was? ### Always, Sometimes or Never? Number

##### Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? ### What Is Ziffle?

##### Age 7 to 11 Challenge Level:

Can you work out what a ziffle is on the planet Zargon? ### Satisfying Statements

##### Age 11 to 14 Challenge Level:

Can you find any two-digit numbers that satisfy all of these statements? ### Digat

##### Age 11 to 14 Challenge Level:

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A ### Factors and Multiples Puzzle

##### Age 11 to 14 Challenge Level:

Using your knowledge of the properties of numbers, can you fill all the squares on the board? ### Divisively So

##### Age 11 to 14 Challenge Level:

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7? ### Oh! Hidden Inside?

##### Age 11 to 14 Challenge Level:

Find the number which has 8 divisors, such that the product of the divisors is 331776. ### It Figures

##### Age 7 to 11 Challenge Level:

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? ### Hot Pursuit

##### Age 11 to 14 Challenge Level:

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same... ### Eminit

##### Age 11 to 14 Challenge Level:

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? ### Thirty Six Exactly

##### Age 11 to 14 Challenge Level:

The number 12 = 2^2 � 3 has 6 factors. What is the smallest natural number with exactly 36 factors? ### Inclusion Exclusion

##### Age 11 to 14 Challenge Level:

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5? ### X Marks the Spot

##### Age 11 to 14 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" . ### Can You Find a Perfect Number?

##### Age 7 to 14

Can you find any perfect numbers? Read this article to find out more... ### Diggits

##### Age 11 to 14 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are? ### Factoring Factorials

##### Age 11 to 14 Challenge Level:

Find the highest power of 11 that will divide into 1000! exactly. ### Dozens

##### Age 7 to 14 Challenge Level:

Do you know a quick way to check if a number is a multiple of two? How about three, four or six? ### Ben's Game

##### Age 11 to 14 Challenge Level:

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. ### Helen's Conjecture

##### Age 11 to 14 Challenge Level:

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true? ### Gaxinta

##### Age 11 to 14 Challenge Level:

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? ### The Remainders Game

##### Age 7 to 14 Challenge Level:

Play this game and see if you can figure out the computer's chosen number. ### Neighbours

##### Age 7 to 11 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square? ### Mathematical Swimmer

##### Age 11 to 14 Challenge Level:

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. . . . ### Surprising Split

##### Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not? ### Counting Cogs

##### Age 7 to 14 Challenge Level:

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?