We can use a rectangle model to represent the relationship between a number and its factors. Suppose you have some tiles; how many rectangles can you form using twelve tiles?
The dimensions of the three rectangles - 1, 2, 3, 4, 6, and 12 - represent the factors of their product, the number 12. We can say that the factors of 12 are 1, 2, 3, 4, 6, and 12.
Factors can be thought of as numbers that can be multiplied together to produce a certain number, or as numbers that can divide evenly into a certain number. Either way, the rectangle models provide a picture of the factor and number relationship.
Sometimes a number has only two factors; that number of tiles can only be formed into one rectangle. Can you think of a few numbers like that? Here is an example:
Since eleven tiles can be arranged into a rectangle in only one way, it has only two factors. Numbers with only two factors are known as prime numbers. Sometimes we say the only two factors are one and the number itself, in this case, eleven.
Factors are a basic part of number sense, and are useful in problem solving. Students and parents can discuss factors of numbers they see on signs, billboards, packaging and many other places, so students can practice and become fluent with determining the factors of various numbers.