Fundamentals of Math

Fundamentals of Mathematics

Next, count up to 2, see if it will divide evenly into the number. If it does then add 2 and the quotient to your list, and if not write nothing and progress again to the next step.

1, 2 __________________________________________________21, 42

Now, count up to 3, again see if it will divide evenly into the number. If it does then add 3 and the quotient to the list, and if not proceed to 4.

1, 2, 3 ___________________________________________14, 21, 42

You will eventually hit the halfway point where the number you are testing is already written in your list and that is how you know you have finished.

Multiples The product of any two factors is a multiple. To find the first multiples of any number start by multiplying the number by 1, then 2, 3, 4, ... . We list these numbers in a line separated by a comma - you will also often see an ellipse (...) written after the last number to indicate the list could continue, but you as the mathematician have chosen to stop listing the multiples. Remember, every real number has an infinite number of multiples.

Example 1.3.3 Find the first five multiples of 13.

1 st

13 × 1 13 × 2 13 × 3 13 × 4 13 × 5

= 13 = 26 = 39 = 52 = 65

2 nd 3 rd 4 th 5 th

The first five multiples of 13 are …

13, 26, 39, 52, 65, …

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