Multiplication and division

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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" .

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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.

Find the next number in this pattern: 3, 7, 19, 55 ...

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?