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?

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

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

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

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" .

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...

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

Number problems at primary level to work on with others.

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.

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?

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

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

Can you work out some different ways to balance this equation?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Number problems at primary level that may require resilience.

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?

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?

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

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

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?

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.

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

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

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. . . .

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.

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?

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.

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

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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

Benâ€™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?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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

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

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

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

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?

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

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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

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

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

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. . . .

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

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?