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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?

Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Unit Fractions

Age 11 to 14 Challenge Level:

Consider the equation ${1\over a} +{1\over b}+{1\over c} = 1$ where $a$, $b$ and $c$ are natural numbers and $0 < a < b < c$. Prove that $a< 3$ and also that $b< 4$ and hence that there is only one set of values which satisfy this equation.

Find the six sets of values which satisfy the equation ${1\over a} +{1\over b}+{1\over c} +{1\over d}= 1$ where $a$, $b$, $c$ and $d$ are natural numbers and $0 < a < b < c < d$.