Factors, Multiples and Primes

Dozens

KS 2 & 3 Challenge Level:

Challenge Level:1

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Statement Snap

KS 2 & 3 Challenge Level:

Challenge Level:1

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

Factors and Multiples Game

KS 2, 3 & 4 Challenge Level:

Challenge Level:1

A game in which players take it in turns to choose a number. Can you block your opponent?

Sieve of Eratosthenes

KS 3 Challenge Level:

Challenge Level:1

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

Multiple Surprises

KS 3 Challenge Level:

Challenge Level:1

Sequences of multiples keep cropping up...

Multiples Sudoku

KS 3 Challenge Level:

Challenge Level:1

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

Gabriel's Problem

KS 3 Challenge Level:

Challenge Level:1

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

How Much Can We Spend?

KS 3 Challenge Level:

Challenge Level:1

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Number Families

KS 3 Challenge Level:

Challenge Level:1

How many different number families can you find?

Factors and Multiples Puzzle

KS 3 Challenge Level:

Challenge Level:1

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

What Numbers Can We Make?

KS 3 Challenge Level:

Challenge Level:1

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

American Billions

KS 3 Challenge Level:

Challenge Level:1

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...

Counting Factors

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

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

Route to Infinity

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

Can you describe this route to infinity? Where will the arrows take you next?

Power Mad!

KS 3 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.

Stars

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Product Sudoku

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

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

Diminishing Returns

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

Alison's Quilt

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

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

Differences

KS 3 Challenge Level:

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

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Funny Factorisation

KS 3 Challenge Level:

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

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

Divisibility Tests

KS 3 & 4

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

Beelines

KS 4 Challenge Level:

Challenge Level:1

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Filling the Gaps

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

Which numbers can we write as a sum of square numbers?

Take Three from Five

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Expenses

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

Latin Numbers

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

Can you create a Latin Square from multiples of a six digit number?