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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.

As Easy as 1,2,3

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type 'TWO' it returns 2, and so on.

Sum Equals Product

Age 11 to 14
Challenge Level


Here are some examples you could try:

$4 + 1 \frac{1}{4}$ and $4 \times 1 \frac{1}{4}$

$5 + 1 \frac{1}{4}$ and $5 \times 1 \frac{1}{4}$

$5 + 1 \frac{1}{5}$ and $5 \times 1 \frac{1}{5}$

$6 + 1 \frac{1}{5}$ and $6 \times 1 \frac{1}{5}$

Which of these give the same answer for both calculations?
Can you use these examples to help you find some more pairs that have the same sum and product?