Welcome to Mathnasium’s Math Tricks series. Today we are using number sense to divide statements where the divisors (the numbers we are dividing by) have more than two factors (numbers which divide evenly into the divisor). Rather than dividing a dividend (the number to be divided) by a challenging divisor, the trick is to break it down into smaller, more manageable parts, and then divide by each part.

Keep in mind: The “commutative” property of multiplication says we can reorder the numbers being multiplied without affecting the answer. So, once we determine the “smaller parts” we want to divide by instead, we can then also choose the order we want to work with. For example, we might not choose to cut an odd number in half first and be left with a fraction if there is another divisor that evenly divides into the odd number.

Use this Mathnasium Math Trick to divide the numbers in the problems below.

##### Example 1: 810 ÷ 45.

**Step 1: Identify the divisor.**
In the above equation, 45 is the divisor.

**Step 2: Break down the divisor into smaller parts, (i.e. identify the factors).**

45 is equal to 3 x 15.

45 is equal to 5 x 9.

45 is equal to 3 x 3 x 5.

**Step 3: Select a group of factors that you can easily divide into the dividend.**
We will work with: 45 is equal to 5 x 9.

**Step 4: Divide the dividend by each factor, in an efficient order.**

810 ÷ 9 = 90

90 ÷ 5 = 18

**Answer:** 18

##### Example 2: 8,640 ÷ 72.

**Step 1: Identify the divisor.**
In the above equation, 72 is the divisor.

**Step 2: Break down the divisor into smaller parts, (i.e. identify the factors).**

72 is equal to 8 x 9.

72 is equal to 3 x 3 x 8.

etc.

**Step 3: Select a group of factors that you can easily divide into the dividend.**
We will work with: 72 is equal to 8 x 9.

**Step 4: Divide the dividend by each factor, in an efficient order.**

8,640 ÷ 8 = 1,080

1,080 ÷ 9 = 120

**Answer:** 120

Now you are ready to divide using your knowledge of breaking apart the divisor. Click here for more practice problems, then check your answers here.

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