# Factors, Multiples and Primes

### Dozens

##### KS 2 & 3 Challenge Level:

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

### Factors and Multiples Game

##### KS 2, 3 & 4 Challenge Level:

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

### Factors and Multiples Puzzle

##### KS 3 Challenge Level:

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:

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:

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...

### Sieve of Eratosthenes

##### KS 3 Challenge Level:

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

### Multiple Surprises

##### KS 3 Challenge Level:

Sequences of multiples keep cropping up...

### Multiples Sudoku

##### KS 3 Challenge Level:

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

### Gabriel's Problem

##### KS 3 Challenge Level:

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:

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:

How many different number families can you find?

### Diminishing Returns

##### KS 3 Challenge Level:

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:

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

### Counting Factors

##### KS 3 Challenge Level:

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

### Route to Infinity

##### KS 3 Challenge Level:

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

##### KS 3 Challenge Level:

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:

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:

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

### Funny Factorisation

##### KS 3 Challenge Level:

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?

### Differences

##### KS 3 Challenge Level:

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

### Beelines

##### KS 4 Challenge Level:

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

### Latin Numbers

##### KS 4 Challenge Level:

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

### Filling the Gaps

##### KS 4 Challenge Level:

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

### Take Three from Five

##### KS 4 Challenge Level:

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:

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