Step 47: Divisors, Factors, and Multiples
Divisors and factors
If a number evenly divides into a number, then it is called a divisor of it. For example, 3 is a divisor of 6 because 3 divides into 6 exactly 2 times. 4 is not a divisor by 6 because it goes into it 1 1/2 times. The word factor means the same thing as divisor.
Common divisors
In some mathematical situations, particularly with simplifying fractions, it is useful to find numbers that evenly divide two given numbers. Such numbers are called common divisors or common factors. The common divisors of 20 and 8 are 1, 2, and 4. You may enjoy exploring together why all the common divisors for a pair of numbers are divisors of the greatest of the common divisors.
Multiples
A multiple of a number is anything that can be produced by multiplying the number by a whole number. For example, some multiples of 6 are 0, 6, 12, and 18. Notice that any multiple of a number has that number as a divisor. For example, each of the multiples of 6 has 6 as a divisor.
Common multiples
A number which is a multiple of two given numbers is said to be a common multiple for them. Some common multiples of 6 and 4 are 0, 12, 24, and 36. Notice that all the common multiples are multiples of the least of the positive common multiples. Common multiples will be useful in adding and subtracting fractions.
Introduce these words
Slowly introduce these new words to your child as you discuss situations that involve multiplication and division. They are useful words that simplify many discussions once the words are understood.