Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples

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?

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?

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?

What Two ...?

Age 7 to 11 Short Challenge Level:

56 406 is the product of two consecutive numbers. What are these two numbers?

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'.

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.

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?

Factoring Factorials

Age 11 to 14 Challenge Level:

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

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.

Product Sudoku

Age 11 to 16 Challenge Level:

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

Counting Cogs

Age 7 to 14 Challenge Level:

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

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?

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?

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?

Venn Diagrams

Age 5 to 11 Challenge Level:

How will you complete these Venn diagrams?

The Remainders Game

Age 7 to 14 Challenge Level:

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

Alison's Quilt

Age 11 to 14 Challenge Level:

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

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!?

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?

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.

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?

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.

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?

A First Product Sudoku

Age 11 to 14 Challenge Level:

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

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?

Multiples Sudoku

Age 11 to 14 Challenge Level:

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

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?

Statement Snap

Age 7 to 14 Challenge Level:

You'll need to know your number properties to win a game of Statement Snap...

Number Families

Age 11 to 14 Challenge Level:

How many different number families can you find?

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?

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?

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.

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?

Guess the Dominoes for Two

Age 7 to 11 Challenge Level:

Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

Transposition Cipher

Age 11 to 16 Challenge Level:

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

Sieve of Eratosthenes

Age 11 to 14 Challenge Level:

Follow this recipe for sieving numbers and see what interesting patterns emerge.

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.

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?

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...

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?

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?

Number Tracks

Age 7 to 11 Challenge Level:

Benâ€™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?

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?

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.

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.

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.

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.

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?