Resources tagged with: Factors and multiples

Filter by: Content type:
Age range:
Challenge level:

There are 154 results

Broad Topics > Properties of Numbers > Factors and multiples

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" .

Times Right

Age 11 to 16
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?

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?

American Billions

Age 11 to 14
Challenge Level

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...

Making Pathways

Age 7 to 11
Challenge Level

Can you find different ways of creating paths using these paving slabs?

The Remainders Game

Age 7 to 14
Challenge Level

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

Multiplication Series: Number Arrays

Age 5 to 11

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

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?

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?

Funny Factorisation

Age 11 to 16
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?

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?

Adding All Nine

Age 11 to 14
Challenge Level

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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?

Big Powers

Age 11 to 16
Challenge Level

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Multiples Sudoku

Age 11 to 14
Challenge Level

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Just Repeat

Age 11 to 14
Challenge Level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Number Detective

Age 5 to 11
Challenge Level

Follow the clues to find the mystery number.

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?

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?

AB Search

Age 11 to 14 Short
Challenge Level

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

Product Sudoku

Age 11 to 16
Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares.

Repeaters

Age 11 to 14
Challenge Level

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.

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.

A First Product Sudoku

Age 11 to 14
Challenge Level

Given the products of adjacent cells, can you complete this Sudoku?

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?

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?

Ben's Game

Age 11 to 16
Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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?

Factoring Factorials

Age 11 to 14
Challenge Level

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

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?

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?

Being Resilient - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level that may require resilience.

Flow Chart

Age 11 to 14
Challenge Level

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

Can You Find a Perfect Number?

Age 7 to 14

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

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...

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?

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?

Odds and Threes

Age 7 to 11
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.

Alison's Quilt

Age 11 to 14
Challenge Level

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

Being Collaborative - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level to work on with others.

Transposition Cipher

Age 11 to 16
Challenge Level

Can you work out what size grid you need to read our secret message?

Satisfying Statements

Age 11 to 14
Challenge Level

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

Always, Sometimes or Never? Number

Age 7 to 11
Challenge Level

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

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?

Multiply Multiples 3

Age 7 to 11
Challenge Level

Have a go at balancing this equation. Can you find different ways of doing it?

Multiply Multiples 2

Age 7 to 11
Challenge Level

Can you work out some different ways to balance this equation?

Multiply Multiples 1

Age 7 to 11
Challenge Level

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Number Families

Age 11 to 14
Challenge Level

How many different number families can you find?

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?

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?