Factors and Multiples

Question

Test each number for divisibility by 11 by alternately adding and subtracting the digits from right to left, beginning with the units digit

—

that is, units digit minus tens digit plus hundreds digit, etc. If the result is divisible by 11, then the original number will be divisible by 11. (Note: Zero is divisible by 11.)

 

Part 1 out of 4

a. 56,975,977

 

Total from alternating adding and subtracting digits: 

Answer 1

Pick some numbers that you know are divisible by 11. like 121. 11 x 11 = 121. Take the digits in 121 which are 1, 2, and 1. Separate them by alternating signs. In the instructions in your problem it says to start between the units digit and the tens digit with a "+" and then alternate. Like this:

I've always done it opposite to this but either way works.

So +1 - 2 + 1 = 0 and 0 is a multiple of 11 so 121 is divisible by 11. (Note that multiples of 11 are things like 11 - 11 or 0; 11 + 11 + 11 or 33; 11 - 11 - 11 or -11.)

Another example, If we multiply 11 x 255 we get 2805 and -2 + 8 - 0 + 5 = 11 and 11 is a multiple of 11 so 2805 is divisible by 11. Another example: 11 x 5489 = 60379. +6 - 0 + 3 - 7 + 9 = 11 and 11 is a multiple of 11 so 60379 is divisible by 11.

Now do the numbers in your problem:

For 56,975,977: -5 + 6 - 9 + 7 - 5 + 9 - 7 + 7 = 3 and 3 is not a multiple of 11 so 56,975,977 is not divisible by 11

Answer 2

The key direction in this problem is "alternately adding and subtracting the digits from right to left, beginning with the units digit." If you follow this procedure and the result is a number divisible by 11, then the number you are testing will be divisible by 11.

Using the number provided, 56,975,977 . . . .

+ 7 (ones column)

-7 (tens column)

___

0

+ 9 (hundreds column)

___

9

-5 (thousands column)

___

4

+ 7 (ten-thousands column)

___

11

-9 (hundred-thousands column)

___

2

+6 (millions column)

___

8

-5 (ten-millions column)

___

3

Since 3 is not divisible by 11, then 56,975,977 is not divisible by 11.

For an example of a number that is divisible by 11, consider 75,977.

+ 7 (ones column)

-7 (tens column)

___

0

+ 9 (hundreds column)

___

9

-5 (thousands column)

___

4

+ 7 (ten-thousands column)

___

11

Since the result is 11, then 75,977 is divisible by 11.