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Resources tagged with Factors and multiples similar to Strange Numbers:

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

Data Chunks

Stage: 4 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. . . .

Different by One

Stage: 4 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)

Number Rules - OK

Stage: 4 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...

Phew I'm Factored

Stage: 4 Challenge 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.

Mod 3

Stage: 4 Challenge Level:

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

Really Mr. Bond

Stage: 4 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?

Ewa's Eggs

Stage: 3 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?

What Numbers Can We Make Now?

Stage: 3 and 4 Challenge Level:

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

Sieve of Eratosthenes

Stage: 3 Challenge Level:

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

Oh! Hidden Inside?

Stage: 3 Challenge Level:

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

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?

Multiplication Magic

Stage: 4 Challenge 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). . . .

Helen's Conjecture

Stage: 3 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?

Common Divisor

Stage: 4 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.

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?

Big Powers

Stage: 3 and 4 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.

For What?

Stage: 4 Challenge Level:

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

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?

Take Three from Five

Stage: 3 and 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?

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?

What a Joke

Stage: 4 Challenge Level:

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

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?

Missing Multipliers

Stage: 3 Challenge Level:

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

Transposition Cipher

Stage: 3 and 4 Challenge Level:

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

A Biggy

Stage: 4 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.

Sixational

Stage: 4 and 5 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. . . .

X Marks the Spot

Stage: 3 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" .

Factoring Factorials

Stage: 3 Challenge Level:

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

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?

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?

Two Much

Stage: 3 Challenge Level:

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

One to Eight

Stage: 3 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.

Powerful Factorial

Stage: 3 Challenge Level:

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!?

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

Divisively So

Stage: 3 Challenge Level:

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

Diggits

Stage: 3 Challenge Level:

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

What Numbers Can We Make?

Stage: 3 Challenge Level:

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

Repeaters

Stage: 3 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.

Three Times Seven

Stage: 3 Challenge Level:

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

Expenses

Stage: 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?

Stars

Stage: 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

Stage: 3, 4 and 5 Challenge Level:

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

LCM Sudoku II

Stage: 3, 4 and 5 Challenge Level:

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

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. . . .

The Remainders Game

Stage: 2 and 3 Challenge Level:

A game that tests your understanding of remainders.

Multiplication Equation Sudoku

Stage: 4 and 5 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.

Factors and Multiples Puzzle

Stage: 3 Challenge Level:

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?