. // factors of a number {questions} {answers}

(1) Is 3 a factor of 24?  Is 8?  How about 14?

Find out by dividing x (the number you are checking) into y (the number you are checking against).  24 / 3 results in an answer of 8, so 3 is a factor of 24.  This check also answers the second question -- since 8 can divide evenly into 24, it too is a factor of 24.  Now let's look at the third question.  Again divide x into y -- 24 / 14 gives you a result of 1.714286.  Since 1.714286 is not an integer, 14 is not a factor of 24.

(2) What are the factors of 36?

When solving problems such as this one, I usually just start at 1 and begin counting.  When the numbers are small, it's easy to figure out whether x will divide into y.  Starting with 1, we can easily see that it is a factor of 36:  36 / 1 = 36.  By looking at this equation, we can also add 36 to our list of factors.  Next we go to 2, and divide it into 36.  36 / 2 = 18, so we can add 2 and 18 to the list.  Continue in this manner with 3, 4, and 6, and by this time your list should be complete -- 1, 2, 3, 4, 6, 9, 12, 18, and 36 are all factors of 36.

(3) How many factors of 28 are -not- also factors of 42?

First, use the method given in problem (2) to determine the factors of 28 and 42.  28's factors are 1, 2, 4, 7, 14, and 28.  42's factors are 1, 2, 3, 6, 7, 14, 21, and 42.  Once we have a factor list for each of these numbers, we can eliminate any numbers that appear on both lists.  Then the only numbers left on 28's list are 4 and 28.  So the answer is 2.