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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

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

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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?

Power Crazy

Age 11 to 14 Challenge Level:

What can you say about the values of n that make 7 n + 3 n a multiple of 10?

Are there other pairs of integers between 1 and 10 which have similar properties?