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

What Two ...?

Stage: 2 Short Challenge Level:

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

Factor Track

Stage: 2 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.

Divide it Out

Stage: 2 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's in the Box?

Stage: 2 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?

Scoring with Dice

Stage: 2 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?

Flashing Lights

Stage: 2 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

Stage: 2 Challenge Level:

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

Which Is Quicker?

Stage: 2 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

What Is Ziffle?

Stage: 2 Challenge Level:

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

Path to the Stars

Stage: 2 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?

Mystery Matrix

Stage: 2 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Becky's Number Plumber

Stage: 2 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?

Zios and Zepts

Stage: 2 Challenge Level:

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?

It Figures

Stage: 2 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?

Times Right

Stage: 3 Challenge Level:

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?

A Mixed-up Clock

Stage: 2 Challenge Level:

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?

Abundant Numbers

Stage: 2 Challenge Level:

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?

Two Primes Make One Square

Stage: 2 Challenge Level:

Can you make square numbers by adding two prime numbers together?

A Dotty Problem

Stage: 2 Challenge Level:

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Sweets in a Box

Stage: 2 Challenge Level:

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Spelling Circle

Stage: 2 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.

The Moons of Vuvv

Stage: 2 Challenge Level:

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Hot Pursuit

Stage: 3 Challenge Level:

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?

Table Patterns Go Wild!

Stage: 2 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.

The Remainders Game

Stage: 2 and 3 Challenge Level:

A game that tests your understanding of remainders.

Which Numbers? (1)

Stage: 2 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)

Stage: 2 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?

Curious Number

Stage: 2 Challenge Level:

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

Gran, How Old Are You?

Stage: 2 Challenge Level:

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Three Spinners

Stage: 2 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?

Stage: 2 Challenge Level:

If you have only four weights, where could you place them in order to balance this equaliser?

Number Tracks

Stage: 2 Challenge Level:

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

Multiplication Squares

Stage: 2 Challenge Level:

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Odds and Threes

Stage: 2 Challenge Level:

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Money Measure

Stage: 2 Challenge Level:

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

Domino Pick

Stage: 2 Challenge Level:

Are these domino games fair? Can you explain why or why not?

Multiplication Series: Number Arrays

Stage: 1 and 2

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

Fitted

Stage: 2 Challenge Level:

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?

Factor-multiple Chains

Stage: 2 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?

One to Eight

Stage: 3 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.

Diggits

Stage: 3 Challenge Level:

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

Down to Nothing

Stage: 2 Challenge Level:

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

Helen's Conjecture

Stage: 3 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?

Oh! Hidden Inside?

Stage: 3 Challenge Level:

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

In the Money

Stage: 2 Challenge Level:

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

Ewa's Eggs

Stage: 3 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?

Gaxinta

Stage: 3 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?

Factor Lines

Stage: 2 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Eminit

Stage: 3 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?