Q:

What are the factors of 48?

A:

The factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. The number 48 is divisible by each of the factors without any remainder being left over.

Finding the factors of a whole number requires some trial and error in the form of a series of division problems. The first two factors in the factor list are the number itself and the number 1. Even numbers like 48 are divisible by 2, so the next step is to calculate the result of dividing 48 by 2, which adds 2 and 24 to the factor list. Since 48 is divisible by 3 with a whole number quotient of 16, 3 and 16 are factors. The process continues by dividing 48 by 4, 5, 6 and so on.

As one works through increasing numbers, the corresponding quotients decrease. At some point, all of the potential whole numbers between 1 and the number are accounted for. When this happens, the last step is to arrange the factors in increasing order.

It is helpful to look at another example to understand factoring more thoroughly. For the number 28, its factors first include 1 and 28. When dividing 28 by 2, the quotient is 14, which means that 2 and 14 are factors. When dividing 28 by 3, the quotient is not a whole number. Moving on to 4, 28 divided by 4 is 7, so 4 and 7 are among its factors. When dividing 28 by 5, the result is not a whole number. To answer the question, the next step is to arrange the factors in order, which results in 1, 2, 4, 7, 14 and 28.


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