# Resources tagged with: Factors and multiples

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### There are 55 results

Broad Topics > Properties of Numbers > Factors and multiples

### Old Nuts

##### Age 16 to 18Challenge Level

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

### Sixational

##### Age 14 to 18Challenge Level

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

### The Public Key

##### Age 16 to 18Challenge Level

Find 180 to the power 59 (mod 391) to crack the code. To find the secret number with a calculator we work with small numbers like 59 and 391 but very big numbers are used in the real world for this.

### Dirisibly Yours

##### Age 16 to 18Challenge Level

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.

### Powerful Factors

##### Age 16 to 18Challenge Level

Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.

### Sums of Squares and Sums of Cubes

##### Age 16 to 18

An account of methods for finding whether or not a number can be written as the sum of two or more squares or as the sum of two or more cubes.

### Some Cubes

##### Age 16 to 18Challenge Level

The sum of the cubes of two numbers is 7163. What are these numbers?

### LCM Sudoku II

##### Age 11 to 18Challenge Level

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

### Really Mr. Bond

##### Age 14 to 16Challenge Level

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

### Telescoping Functions

##### Age 16 to 18

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.

### Multiplication Magic

##### Age 14 to 16Challenge Level

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .

### Em'power'ed

##### Age 16 to 18Challenge Level

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

### Polite Numbers

##### Age 16 to 18Challenge Level

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?

### Public Key Cryptography

##### Age 16 to 18

An introduction to coding and decoding messages and the maths behind how to secretly share information.

### Data Chunks

##### Age 14 to 16Challenge Level

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

### Take Three from Five

##### Age 11 to 16Challenge 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?

### Mod 3

##### Age 14 to 16Challenge Level

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

### Divisibility Tests

##### Age 11 to 16

This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

### Number Rules - OK

##### Age 14 to 16Challenge Level

Can you produce convincing arguments that a selection of statements about numbers are true?

### Common Divisor

##### Age 14 to 16Challenge Level

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

### A Biggy

##### Age 14 to 16Challenge Level

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

### Funny Factorisation

##### Age 11 to 16Challenge Level

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

### N000ughty Thoughts

##### Age 14 to 16Challenge Level

How many noughts are at the end of these giant numbers?

### Squaresearch

##### Age 14 to 16Challenge Level

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

### Why 24?

##### Age 14 to 16Challenge Level

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

### Beelines

##### Age 14 to 16Challenge Level

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

### What a Joke

##### Age 14 to 16Challenge Level

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

### Big Powers

##### Age 11 to 16Challenge 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.

### Hypotenuse Lattice Points

##### Age 14 to 16Challenge Level

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

### Expenses

##### Age 14 to 16Challenge Level

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

### Fac-finding

##### Age 14 to 16Challenge Level

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

### DOTS Division

##### Age 14 to 16Challenge Level

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

### Phew I'm Factored

##### Age 14 to 16Challenge Level

Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.

### Transposition Cipher

##### Age 11 to 16Challenge Level

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

### There's Always One Isn't There

##### Age 14 to 16Challenge Level

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

### Star Product Sudoku

##### Age 11 to 16Challenge 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.

### Factors and Multiples - Secondary Resources

##### Age 11 to 16Challenge Level

A collection of resources to support work on Factors and Multiples at Secondary level.

### Different by One

##### Age 14 to 16Challenge Level

Can you make lines of Cuisenaire rods that differ by 1?

### Diagonal Product Sudoku

##### Age 11 to 16Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku?

### Times Right

##### Age 11 to 16Challenge 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?

### Product Sudoku

##### Age 11 to 16Challenge Level

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

### Rarity

##### Age 16 to 18Challenge Level

Show that it is rare for a ratio of ratios to be rational.

### Ben's Game

##### Age 11 to 16Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

### Factoring a Million

##### Age 14 to 16Challenge Level

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

### Factorial Fun

##### Age 16 to 18Challenge Level

How many divisors does factorial n (n!) have?

### LCM Sudoku

##### Age 14 to 16Challenge Level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

### Factorial

##### Age 14 to 16Challenge Level

How many zeros are there at the end of the number which is the product of first hundred positive integers?