# Resources tagged with: Factors and multiples

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Broad Topics > Numbers and the Number System > Factors and multiples ### The Remainders Game

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

Play this game and see if you can figure out the computer's chosen 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... ### Factors and Multiples - Secondary Resources

##### Age 11 to 16 Challenge Level:

A collection of resources to support work on Factors and Multiples at Secondary level. ### 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. ### 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. ### Powerful Factorial

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

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!? ### 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? ### Remainder

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

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2? ### 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? ### What Two ...?

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

56 406 is the product of two consecutive numbers. What are these two 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? ### A First Product Sudoku

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

Given the products of adjacent cells, can you complete this Sudoku? ##### Age 11 to 14 Challenge 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? ##### Age 11 to 16 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be? ### Factor Track

##### Age 7 to 14 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. ### 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? ### Counting Factors

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

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not? ### 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? ### Diagonal Product Sudoku

##### Age 11 to 16 Challenge Level:

Given the products of diagonally opposite cells - can you complete this Sudoku? ### 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? ### Got It

##### Age 7 to 14 Challenge 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. ### 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. ### Factoring Factorials

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

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

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six? ### 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? ### 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? ### Can You Find a Perfect Number?

##### Age 7 to 14 ### Gaxinta

##### Age 11 to 14 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? ### 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? ### Two Much

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

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears. ### Mathematical Swimmer

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

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . . ### 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? ### 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? ### Stars

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit? ### 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? ### 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? ### AB Search

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

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

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

Can you find a way to identify times tables after they have been shifted up or down? ### 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? ### Cuboids

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all? ### Star Product Sudoku

##### Age 11 to 16 Challenge 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. ### 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. ### 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? ### 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... ### 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? ### 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. ### 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?