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Counting Factors

Is there an efficient way to work out how many factors a large number has?

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Times Right

Age 11 to 16 Challenge Level:

Fill these boxes with the digits 1, 2, 3, 4, 5, 6, 7 and 8 using each digit only once, so that the expression is correct. How many different solutions can you find?

Is it possible to do this with the digits 0 to 7? What about using the digits 2 to 9?

Printable NRICH Roadshow resource.