Multiplication and division

problem
Expenses

Age

14 to 16

Challenge level

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 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?
problem
Oh! Hidden inside?

Age

11 to 14

Challenge level

Find the number which has 8 divisors, such that the product of the divisors is 331776.
problem
Repeaters

Age

11 to 14

Challenge level

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
problem
More mods

Age

14 to 16

Challenge level

What is the units digit for the number 123^(456) ?
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
The puzzling sweet shop

Age

5 to 11

Challenge level

There were cola bottles for 2p, mini eggs for 3p, marshmallow twists for 5p and lollipops for 7p in the sweet shop. What could each of the children buy with their money?
problem
What's my weight?

Age

7 to 11

Challenge level

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
problem
Catrina's cards

Age

5 to 7

Challenge level

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

Age

7 to 11

Challenge level

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?