Prime numbers

problem
Tom's number

Age

7 to 11

Challenge level

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
problem
Powerful factorial

Age

11 to 14

Challenge level

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
Great Granddad

Age

11 to 14

Challenge level

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
problem
Factoring a million

Age

14 to 16

Challenge level

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
problem
One to eight

Age

11 to 14

Challenge level

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
Why 24?

Age

14 to 16

Challenge level

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
problem
Factoring factorials

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.
problem
Never prime

Age

14 to 16

Challenge level

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
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?