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Counting Factors

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

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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?

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Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

Two Much

Age 11 to 14 Challenge Level:

Explain why the arithmetic sequence

1, 14, 27, 40, ...

contains many terms of the form 222...2 where only the digit 2 appears. How many twos appear in these terms?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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