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We hope that if you decided you didn’t know any number systems other than decimals, you were disabused of that notion promptly. There are many common ways to represent quantities other than with ten digits. Most of us can read Roman numerals and tally marks, for example.

Some number systems use more than ten different digits, and some fewer. For example, ancient Babylonians used a system with sixty different signs. Modern electronic computers, on the other hand, usually use a system with only two different numerals, 0 and 1. To understand how arithmetic can be done in such a system, we first must thoroughly understand how arithmetic is done with our decimal system numbers.

First let’s review some terms used in arithmetic, and in particular multiplication. There are some whole numbers that can be formed by multiplication of other whole numbers. The number 6, for example, is the product resulting from the multiplication of 2 and 3. That is, 2 × 3 = 6. In such a multiplication, 6 is the product and the numbers 2 and 3 are called factors of 6.

Similarly, 5 × 7 = 35; 35 is the product and 5 and 7 are the factors that were multiplied together to form the product.

Which sets of numbers below are the factors of the number 15?