# Resources tagged with: Factors and multiples

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Broad Topics > Numbers and the Number System > Factors and multiples ### Surprising Split

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not? ### 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? ### 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? ### 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? ### 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? ### Being Resilient - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience. ### 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? ### 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? ### 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'. ### Zios and Zepts

##### Age 7 to 11 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? ### 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? ### 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? ### 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? ### 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? ### Abundant Numbers

##### Age 7 to 11 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? ### 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? ### 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? ### The Remainders Game

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

Play this game and see if you can figure out the computer's chosen 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? ### Being Collaborative - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level to work on with others. ### 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? ### 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. ### 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? ### 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? ### 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. ### 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? ### 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. ### Down to Nothing

##### Age 7 to 11 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. ### A First Product Sudoku

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

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

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

Is there an efficient way to work out how many factors a large number has? ### 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. ### Making Pathways

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

Can you find different ways of creating paths using these paving slabs? ### 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? ### 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? ##### Age 7 to 11 Challenge Level:

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

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

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

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

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

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

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

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why? ### 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... ### 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. ### 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? ### 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? ### Factoring Factorials

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

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

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

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