# Search by Topic

#### Resources tagged with Factors and multiples similar to Andy's Marbles:

Filter by: Content type:
Stage:
Challenge level:

### There are 140 results

Broad Topics > Numbers and the Number System > Factors and multiples

### Red Balloons, Blue Balloons

##### Stage: 2 Challenge Level:

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

### Mathematical Swimmer

##### Stage: 3 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. . . .

### In the Money

##### Stage: 2 Challenge Level:

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

##### Stage: 3 Challenge Level:

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

### Flashing Lights

##### Stage: 2 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?

### Abundant Numbers

##### Stage: 2 Challenge Level:

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

### Multiplication Series: Number Arrays

##### Stage: 1 and 2

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

### Factoring Factorials

##### Stage: 3 Challenge Level:

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

### Round and Round the Circle

##### Stage: 2 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

### Ben's Game

##### Stage: 3 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.

### What's in the Box?

##### Stage: 2 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?

### Zios and Zepts

##### Stage: 2 Challenge Level:

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

### Shifting Times Tables

##### Stage: 3 Challenge Level:

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

### Tiling

##### Stage: 2 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

### Three Spinners

##### Stage: 2 Challenge Level:

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

### Spelling Circle

##### Stage: 2 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.

### Crossings

##### Stage: 2 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?

### Money Measure

##### Stage: 2 Challenge Level:

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

### Eminit

##### Stage: 3 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?

### Thirty Six Exactly

##### Stage: 3 Challenge Level:

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

### Divide it Out

##### Stage: 2 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?

### Scoring with Dice

##### Stage: 2 Challenge Level:

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

### Hot Pursuit

##### Stage: 3 Challenge Level:

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

### American Billions

##### Stage: 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...

### Inclusion Exclusion

##### Stage: 3 Challenge Level:

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

### Which Is Quicker?

##### Stage: 2 Challenge Level:

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

### Number Tracks

##### Stage: 2 Challenge Level:

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

### 14 Divisors

##### Stage: 3 Challenge Level:

What is the smallest number with exactly 14 divisors?

### Fractions in a Box

##### Stage: 2 Challenge Level:

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

### Times Right

##### Stage: 3 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?

### AB Search

##### Stage: 3 Challenge Level:

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

### What Two ...?

##### Stage: 2 Short Challenge Level:

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

### Path to the Stars

##### Stage: 2 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?

### Gaxinta

##### Stage: 3 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?

### Digat

##### Stage: 3 Challenge Level:

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

### Special Sums and Products

##### Stage: 3 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

### Becky's Number Plumber

##### Stage: 2 Challenge Level:

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

### Funny Factorisation

##### Stage: 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. . . .

### Diggits

##### Stage: 3 Challenge Level:

Can you find what the last two digits of the number $4^{1999}$ are?

### Dozens

##### Stage: 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?

### Remainders

##### Stage: 3 Challenge Level:

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

### Sieve of Eratosthenes

##### Stage: 3 Challenge Level:

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

### Factor Track

##### Stage: 2 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.

### Oh! Hidden Inside?

##### Stage: 3 Challenge Level:

Find the number which has 8 divisors, such that the product of the divisors is 331776.

### Counting Cogs

##### Stage: 2 and 3 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?

### Three Dice

##### Stage: 2 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

### Which Numbers? (1)

##### Stage: 2 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?

### Remainder

##### Stage: 3 Challenge Level:

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

### Which Numbers? (2)

##### Stage: 2 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?