 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 5, Part B:
Divisibility Tests

In This Part: Developing Testing Rules | Divisibility Tests for 2, 5, and 10
Divisibility Tests for 3 and 9 | Divisibility Tests for 4 and 8 | Divisibility Test for 11

You probably used the test for 2 and the test for 3 to check divisibility by 6. We cannot, however, use the test for 2 twice to check for divisibility by 4. Using 2 and 3 works because they are relatively prime; that is, the only factor they have in common is 1.

The test for divisibility by 2 can be modified for testing divisibility by 4 and 8. Here's how it works.

Since 4 does not divide 10, but 4 does divide 100, rewrite the number, such as the five-digit number abcde, into two parts, abc00 + de; this is 100 times the three-digit number abc plus the two-digit number de. Since 4 divides 100, then 4 divides abc00, and all that needs to be checked is the two-digit number de. If de is divisible by 4, then the entire number is divisible by 4.

For example, to check whether the number 23,456 is divisible by 4, rewrite the number as 23,400 + 56. We know that 4 divides 23,400. Since 4 also divides 56, then 4 divides 23,456.

The test for divisibility by 8 continues this pattern. Because 8 does not evenly divide either 10 or 100, but it does divide 1,000, separate the number -- for example, separate abcde into two parts, ab000 + cde. To test 23,456, write the numbers 23,000 + 456. Since 8 divides 23,000 and 8 divides 456, then 8 evenly divides 23,456.

You can try these tests with the numbers in the chart below:  Row Numbers   1 1 11 21 31 151 2461 10,561 2 2 12 22 32 152 2462 10,562 3 3 13 23 33 153 2463 10,563 4 4 14 24 34 154 2464 10,564 5 5 15 25 35 155 2465 10,565 6 6 16 26 36 156 2466 10,566 7 7 17 27 37 157 2467 10,567 8 8 18 28 38 158 2468 10,568 9 9 19 29 39 159 2469 10,569 10 10 20 30 40 160 2470 10,570 Blue: Divisible by 4, but not 8
Red: Divisible by 4 and 8 Problem B5 Use the divisibility test to determine whether the following numbers are divisible by 4 and 8:

 a. 32,464 b. 82,426   Video Segment In this video segment, Rhonda and Andrea explain how they found the test for divisibility by 4. They then extend the same reasoning to discover the divisibility test for 8 and other powers of 2. If you are using a VCR, you can find this segment on the session video approximately 9 minutes and 31 seconds after the Annenberg Media logo.      Session 5: Index | Notes | Solutions | Video