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

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" .

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

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.

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?

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

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?

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.

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

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

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. . . .

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

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?

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

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?

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

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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

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?

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

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

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

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?

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?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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

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?

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

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

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!?

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

Number problems at primary level to work on with others.

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

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. . . .

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Can you find different ways of creating paths using these paving slabs?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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?

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

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

Number problems at primary level that may require resilience.