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Special Sums and Products

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Sum Equals Product

Age 11 to 14 Challenge Level:

The sum of the numbers 4 and $1 \frac{1}{3}$ is the same as the product of 4 and $1 \frac{1}{3}$;
that is to say $4 +\frac{4}{3} = 4 \times \frac{4}{3}$.

What other numbers have the sum equal to the product?

What relationship must exist between the numbers?