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Resources tagged with Factors and multiples similar to Sixational:

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

Age 14 to 18 Challenge 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. . . . A Biggy

Age 14 to 16 Challenge 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. For What?

Age 14 to 16 Challenge Level:

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares. Mod 3

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge 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. N000ughty Thoughts

Age 14 to 16 Challenge Level:

How many noughts are at the end of these giant numbers? Take Three from Five

Age 14 to 16 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? Age 11 to 14 Challenge Level:

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. . . . Star Product Sudoku

Age 11 to 16 Challenge 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. One to Eight

Age 11 to 14 Challenge Level:

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. Really Mr. Bond

Age 14 to 16 Challenge 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? Age 11 to 14 Challenge Level:

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it? Three Times Seven

Age 11 to 14 Challenge Level:

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

Age 14 to 16 Challenge Level:

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number... Special Sums and Products

Age 11 to 14 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. Hot Pursuit

Age 11 to 14 Challenge Level:

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same... What Numbers Can We Make?

Age 11 to 14 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make? Even So

Age 11 to 14 Challenge Level:

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? Helen's Conjecture

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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. Counting Factors

Age 11 to 14 Challenge Level:

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

Age 7 to 14 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win? Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target? Times Right

Age 11 to 16 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? Big Powers

Age 11 to 16 Challenge 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. AB Search

Age 11 to 14 Challenge Level:

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

Age 7 to 14 Challenge Level:

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be? Eminit

Age 11 to 14 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? Inclusion Exclusion

Age 11 to 14 Challenge Level:

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5? Can You Find a Perfect Number?

Age 7 to 14 Got It

Age 7 to 14 Challenge Level:

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. What a Joke

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge 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. . . . LCM Sudoku II

Age 11 to 18 Challenge Level:

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

Age 7 to 14 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. Sieve of Eratosthenes

Age 11 to 14 Challenge Level:

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

Age 11 to 16 Challenge Level:

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

Age 11 to 16 Challenge Level:

How did the the rotation robot make these patterns? Different by One

Age 14 to 16 Challenge Level:

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod) Factorial

Age 14 to 16 Challenge Level:

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

Age 11 to 14 Challenge Level:

Can you find any two-digit numbers that satisfy all of these statements? Remainder

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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? Digat

Age 11 to 14 Challenge Level:

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

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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" . Divisively So

Age 11 to 14 Challenge Level:

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