Search by Topic

Resources tagged with Factors and multiples similar to Can You Find a Perfect Number?:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 145 results

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

problem icon

Can You Find a Perfect Number?

Stage: 2 and 3

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

problem icon

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?

problem icon

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.

problem icon

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?

problem icon

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" .

problem icon

Three Dice

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

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.

problem icon

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?

problem icon

What Do You Need?

Stage: 2 Challenge Level: Challenge Level:1

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

problem icon

Crossings

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

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?

problem icon

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. . . .

problem icon

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?

problem icon

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?

problem icon

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?

problem icon

Three Neighbours

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

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

problem icon

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.

problem icon

Path to the Stars

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

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?

problem icon

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?

problem icon

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?

problem icon

Factor Track

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

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.

problem icon

Times Right

Stage: 3 and 4 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?

problem icon

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 I. . . .

problem icon

GOT IT Now

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

problem icon

The Moons of Vuvv

Stage: 2 Challenge Level: Challenge Level:1

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

problem icon

Round and Round the Circle

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

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.

problem icon

Always, Sometimes or Never? Number

Stage: 2 Challenge Level: Challenge Level:1

Are these statements always true, sometimes true or never true?

problem icon

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.

problem icon

Spelling Circle

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

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

problem icon

Factors and Multiple Challenges

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

problem icon

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?

problem icon

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.

problem icon

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?

problem icon

14 Divisors

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

What is the smallest number with exactly 14 divisors?

problem icon

Sieve of Eratosthenes

Stage: 3 Challenge Level: Challenge Level:1

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

problem icon

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?

problem icon

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?

problem icon

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

problem icon

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!?

problem icon

Which Numbers? (1)

Stage: 2 Challenge Level: Challenge Level:1

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?

problem icon

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?

problem icon

Which Numbers? (2)

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

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

problem icon

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?

problem icon

Colour Wheels

Stage: 2 Challenge Level: Challenge Level:1

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

problem icon

Which Is Quicker?

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

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?

problem icon

A First Product Sudoku

Stage: 3 Challenge Level: Challenge Level:1

Given the products of adjacent cells, can you complete this Sudoku?

problem icon

Hidden Squares

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

problem icon

Number Tracks

Stage: 2 Challenge Level: Challenge Level:1

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

problem icon

Scoring with Dice

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

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?

problem icon

Times Tables Shifts

Stage: 2 Challenge Level: Challenge Level:1

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?