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Broad Topics > Numbers and the Number System > Factors and multiples Factor Track

Age 7 to 14 Challenge Level:

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules. Remainders

Age 7 to 14 Challenge Level:

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be? 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? Sieve of Eratosthenes

Age 11 to 14 Challenge Level:

Follow this recipe for sieving numbers and see what interesting patterns emerge. Remainder

Age 11 to 14 Challenge Level:

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2? Ewa's Eggs

Age 11 to 14 Challenge Level:

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? Surprising Split

Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not? One to Eight

Age 11 to 14 Challenge Level:

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. 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? Two Much

Age 11 to 14 Challenge Level:

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears. 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? Diggits

Age 11 to 14 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are? Satisfying Statements

Age 11 to 14 Challenge Level:

Can you find any two-digit numbers that satisfy all of these statements? 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? 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? 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. 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? What Two ...?

Age 7 to 11 Short Challenge Level:

56 406 is the product of two consecutive numbers. What are these two numbers? What Is Ziffle?

Age 7 to 11 Challenge Level:

Can you work out what a ziffle is on the planet Zargon? 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? AB Search

Age 11 to 14 Challenge Level:

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B? 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? 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? 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'. Counting Factors

Age 11 to 14 Challenge Level:

Is there an efficient way to work out how many factors a large number has? 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? Factoring Factorials

Age 11 to 14 Challenge Level:

Find the highest power of 11 that will divide into 1000! exactly. 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? 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. . . . 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? 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? 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? Powerful Factorial

Age 11 to 14 Challenge Level:

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!? Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true? 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? 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? Funny Factorisation

Age 11 to 14 Challenge Level:

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors? Digat

Age 11 to 14 Challenge Level:

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A 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? 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. Missing Multipliers

Age 7 to 14 Challenge Level:

What is the smallest number of answers you need to reveal in order to work out the missing headers? 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... What Numbers Can We Make Now?

Age 11 to 14 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now? Even So

Age 11 to 14 Challenge Level:

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? Scoring with Dice

Age 7 to 11 Challenge Level:

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. 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? 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? 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. Number Tracks

Age 7 to 11 Challenge Level:

Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see? Can You Find a Perfect Number?

Age 7 to 14

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