# Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples ### Repeaters

##### Age 11 to 14Challenge 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. ### Hot Pursuit

##### Age 11 to 14Challenge 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... ### Summing Consecutive Numbers

##### Age 11 to 14Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers? ### Counting Factors

##### Age 11 to 14Challenge Level

Is there an efficient way to work out how many factors a large number has? ### Times Right

##### Age 11 to 16Challenge 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? ### Just Repeat

##### Age 11 to 14Challenge 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? ### Big Powers

##### Age 11 to 16Challenge 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. ### Three Times Seven

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge 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? ##### Age 11 to 14Challenge Level

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it? ### Funny Factorisation

##### Age 11 to 16Challenge Level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors? ### Special Sums and Products

##### Age 11 to 14Challenge Level

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48. ##### Age 11 to 14Challenge 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. . . . ### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now? ### Have You Got It?

##### Age 11 to 14Challenge Level

Can you explain the strategy for winning this game with any target? ### Got it for Two

##### Age 7 to 14Challenge Level

Got It game for an adult and child. How can you play so that you know you will always win? ### Gabriel's Problem

##### Age 11 to 14Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was? ### Can You Find a Perfect Number?

##### Age 7 to 14 ### Inclusion Exclusion

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

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors? ### Eminit

##### Age 11 to 14Challenge 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? ### American Billions

##### Age 11 to 14Challenge 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... ### Multiples Sudoku

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

Find the highest power of 11 that will divide into 1000! exactly. ### A First Product Sudoku

##### Age 7 to 14Challenge Level

Given the products of adjacent cells, can you complete this Sudoku? ### Always, Sometimes or Never? Number

##### Age 7 to 11Challenge Level

Are these statements always true, sometimes true or never true? ### AB Search

##### Age 11 to 14 ShortChallenge Level

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

##### Age 11 to 14Challenge Level

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

##### Age 11 to 16Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku? ### Mystery Matrix

##### Age 7 to 11Challenge Level

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

##### Age 7 to 14Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target. ### 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. ### Factor Track

##### Age 7 to 14Challenge 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. ### Multiply Multiples 3

##### Age 7 to 11Challenge Level

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

##### Age 7 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

How many different number families can you find? ### Multiply Multiples 1

##### Age 7 to 11Challenge Level

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

##### Age 11 to 14Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make? ### Three Dice

##### Age 7 to 11Challenge Level

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice? ### Multiply Multiples 2

##### Age 7 to 11Challenge Level

Can you work out some different ways to balance this equation? ### Exploring Simple Mappings

##### Age 11 to 14Challenge Level

Explore the relationship between simple linear functions and their graphs. ### Crossings

##### Age 7 to 11Challenge 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? ### Counting Cogs

##### Age 7 to 14Challenge Level

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why? ### Surprising Split

##### Age 7 to 11Challenge Level

Does this 'trick' for calculating multiples of 11 always work? Why or why not? ### The Moons of Vuvv

##### Age 7 to 11Challenge Level

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

##### Age 7 to 14Challenge Level

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

##### Age 7 to 11Challenge Level

Can you find different ways of creating paths using these paving slabs? ### Star Product Sudoku

##### Age 11 to 16Challenge Level

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid. ### Product Sudoku

##### Age 11 to 16Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares. ### Alison's Quilt

##### Age 11 to 14Challenge Level

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