Prime numbers

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
Just repeat

Age

11 to 14

Challenge level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
problem
There's always one isn't there

Age

14 to 16

Challenge level

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
problem
Rarity

Age

16 to 18

Challenge level

Show that it is rare for a ratio of ratios to be rational.
problem
Three primes

Age

14 to 16

Challenge level

Weekly Problem 6 - 2010
Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?
problem
HCF expression

Age

11 to 14

Challenge level

Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.
problem
What's left?

Age

5 to 7

Challenge level

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
problem
Numbers as shapes

Age

5 to 7

Challenge level

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
game
Favourite

Dicey array

Age

5 to 11

Challenge level

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?
problem
Swimming pool tiles

Age

7 to 11

Challenge level

This activity creates an opportunity to explore all kinds of number-related patterns.