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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?

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?

One to Eight

Age 11 to 14 Challenge Level:

Expressing the four digit numbers as the product of their prime factors may help you narrow down the options.

The units digit of the factors will determine the units digit of the product.