Multiplication and division

problem
Factoring factorials

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.
problem
Eminit

Age

11 to 14

Challenge level

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?
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
X marks the spot

Age

11 to 14

Challenge level

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" .
problem
A one in seven chance

Age

11 to 14

Challenge level

What is the remainder when 2^{164}is divided by 7?
problem
Catrina's cards

Age

5 to 7

Challenge level

How would you find out how many football cards Catrina has collected?
problem
Share bears

Age

5 to 7

Challenge level

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
problem
Shut the box

Age

5 to 7

Challenge level

An old game with lots of arithmetic!
problem
Lots of biscuits!

Age

5 to 7

Challenge level

Help share out the biscuits the children have made.