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Resources tagged with Factors and multiples similar to Not a Polite Question:

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

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Thirty Six Exactly

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

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

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Times Right

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

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?

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One to Eight

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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Helen's Conjecture

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

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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Oh! Hidden Inside?

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

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

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Can You Find a Perfect Number?

Stage: 2 and 3

Can you find any perfect numbers? Read this article to find out more...

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AB Search

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

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

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X Marks the Spot

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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Phew I'm Factored

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Divisively So

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

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

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Really Mr. Bond

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Remainders

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

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?

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Big Powers

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

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.

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Eminit

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

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?

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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?

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Missing Multipliers

Stage: 3 Challenge Level: Challenge Level:1

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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Sieve of Eratosthenes

Stage: 3 Challenge Level: Challenge Level:1

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

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Mathematical Swimmer

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

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. . . .

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Shifting Times Tables

Stage: 3 Challenge Level: Challenge Level:1

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

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Inclusion Exclusion

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

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

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What a Joke

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

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

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Hot Pursuit

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

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?

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Multiplication Magic

Stage: 4 Challenge Level: Challenge Level:1

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). . . .

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Digat

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

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

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Ewa's Eggs

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

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

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Reverse to Order

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

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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Gaxinta

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

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?

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Diggits

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

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

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Even So

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

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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Adding All Nine

Stage: 3 Challenge Level: Challenge Level:1

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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Repeaters

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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LCM Sudoku II

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

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

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Product Sudoku 2

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

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

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Factorial

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

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

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Napier's Location Arithmetic

Stage: 4 Challenge Level: Challenge Level:1

Have you seen this way of doing multiplication ?

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Three Times Seven

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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Factoring Factorials

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

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

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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.

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Multiplication Equation Sudoku

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Exploring Simple Mappings

Stage: 3 Challenge Level: Challenge Level:1

Explore the relationship between simple linear functions and their graphs.

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The Remainders Game

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

A game that tests your understanding of remainders.

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Two Much

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

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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Remainder

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

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

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Powerful Factorial

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

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

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LCM Sudoku

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

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

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Transposition Cipher

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

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

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What Numbers Can We Make Now?

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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Got It

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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Cuboids

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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Squaresearch

Stage: 4 Challenge Level: Challenge Level:1

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


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