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Broad Topics > Calculations and Numerical Methods > Multiplication & division

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Diggits

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Largest Number

Stage: 3 Challenge Level: Challenge Level:1

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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Two Many

Stage: 3 Challenge Level: Challenge Level:1

What is the least square number which commences with six two's?

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Please Explain

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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Slippy Numbers

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

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Times Right

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Like Powers

Stage: 3 Challenge Level: Challenge Level:1

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

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As Easy as 1,2,3

Stage: 3 Challenge Level: Challenge Level:1

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

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Power Mad!

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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Round and Round and Round

Stage: 3 Challenge Level: Challenge Level:1

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

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Long Multiplication

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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Remainders

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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A Chance to Win?

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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A One in Seven Chance

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the remainder when 2^{164}is divided by 7?

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Method in Multiplying Madness?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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I'm Eight

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

Find a great variety of ways of asking questions which make 8.

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Missing Multipliers

Stage: 3 Challenge Level: Challenge Level:1

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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X Marks the Spot

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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" .

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Ordering Cards

Stage: 1 and 2 Challenge Level: Challenge Level:1

This problem is designed to help children to learn, and to use, the two and three times tables.

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Eminit

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Square Subtraction

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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Napier's Bones

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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All the Digits

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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Divide it Out

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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What's My Weight?

Stage: 2 Short Challenge Level: Challenge Level:1

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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Clever Santa

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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What's in the Box?

Stage: 2 Challenge Level: Challenge Level:1

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?

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The Deca Tree

Stage: 2 Challenge Level: Challenge Level:1

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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Four Goodness Sake

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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Practice Run

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

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Tom's Number

Stage: 2 Challenge Level: Challenge Level:1

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

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Factor-multiple Chains

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Repeaters

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Watching the Wheels Go 'round and 'round

Stage: 2 Challenge Level: Challenge Level:1

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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Difficulties with Division

Stage: 1 and 2

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

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Fair Feast

Stage: 2 Challenge Level: Challenge Level:1

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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Learning Times Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

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Jumping

Stage: 2 Challenge Level: Challenge Level:1

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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Which Is Quicker?

Stage: 2 Challenge Level: Challenge Level:1

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

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Current Playing with Number Upper Primary Teacher

Stage: 2 Challenge Level: Challenge Level:1

Resources to support understanding of multiplication and division through playing with number.

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What Is Ziffle?

Stage: 2 Challenge Level: Challenge Level:1

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

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Multiply Multiples 3

Stage: 2 Challenge Level: Challenge Level:1

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

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Multiply Multiples 2

Stage: 2 Challenge Level: Challenge Level:1

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

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Multiply Multiples 1

Stage: 2 Challenge Level: Challenge Level:1

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

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Escape from the Castle

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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Sort Them Out (2)

Stage: 2 Challenge Level: Challenge Level:1

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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One Million to Seven

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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A First Product Sudoku

Stage: 3 Challenge Level: Challenge Level:1

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

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Magic Potting Sheds

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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Cows and Sheep

Stage: 2 Challenge Level: Challenge Level:1

Use your logical reasoning to work out how many cows and how many sheep there are in each field.