Multiplication and division

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
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
Calendar calculations

Age

7 to 11

Challenge level

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
problem
Code breaker

Age

7 to 11

Challenge level

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
problem
Sept03 Sept03 Sept03

Age

7 to 11

Challenge level

This number has 903 digits. What is the sum of all 903 digits?
problem
Adjacent factors

Age

11 to 14

Challenge level

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?
problem
Rolling along the trail

Age

11 to 14

Challenge level

What could be the scores from five throws of this dice?
problem
Napier's bones

Age

7 to 11

Challenge level

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
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
ABC

Age

7 to 11

Challenge level

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?