Factors, Multiples and Primes

14 Divisors

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What is the smallest number with exactly 14 divisors?

Dozens

Stage: 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?

Expenses

Stage: 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?

Differences

Stage: 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

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

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can you find the factors?

American Billions

Stage: 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...

Divisibility Tests

Stage: 3, 4 and 5

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

Take Three from Five

Stage: 3 and 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?

Stars

Stage: 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

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

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

Factors and Multiples Puzzle

Stage: 3 Challenge Level: Challenge Level:1

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

Factors and Multiples Game

Stage: 2 and 3 Challenge Level: Challenge Level:1

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

Power Mad!

Stage: 3 and 4 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.

How Much Can We Spend?

Stage: 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?

Counting Cogs

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

What Numbers Can We Make?

Stage: 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?

Sieve of Eratosthenes

Stage: 3 Challenge Level: Challenge Level:1

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

Filling the Gaps

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Factors, Multiples and Primes - Short Problems

Stage: 3 and 4 Challenge Level: Challenge Level:1

A collection of short Stage 3 and 4 problems on factors, multiples and primes.