Multiplication and division

problem
Favourite

More Magic Potting Sheds

Age

11 to 16

Challenge level

3 out of 3

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
problem
Favourite

Expenses

Age

14 to 16

Challenge level

2 out of 3

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?
problem

As Easy as 1,2,3

Age

11 to 14

Challenge level

1 out of 3

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type 'TWO' it returns 2, and so on.
problem

Two Many

Age

11 to 14

Challenge level

1 out of 3

What is the least square number which commences with six two's?
problem

Machines

Age

7 to 11

Challenge level

1 out of 3

What is happening at each box in these machines?
problem

More Mods

Age

14 to 16

Challenge level

2 out of 3

What is the units digit for the number 123^(456) ?
problem

Repeaters

Age

11 to 14

Challenge level

2 out of 3

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

Thirty Six Exactly

Age

11 to 14

Challenge level

2 out of 3

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

2 out of 3

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

2 out of 3

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?