Multiplication and division

problem
Ones only

Age

11 to 14

Challenge level

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
problem
Book codes

Age

7 to 11

Challenge level

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
problem
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?
problem
Sam's quick sum

Age

7 to 11

Challenge level

What is the sum of all the three digit whole numbers?
problem
As easy as 1,2,3

Age

11 to 14

Challenge level

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type 'TWO' it returns 2, and so on.
problem
Thirty six exactly

Age

11 to 14

Challenge level

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
problem
The 24 game

Age

7 to 11

Challenge level

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
problem
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?
problem
Expenses

Age

14 to 16

Challenge level

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?
problem
Legs eleven

Age

11 to 14

Challenge level

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?