Question

4. Without performing the divisions, determine whether the integers 176521221 and 149235678 are divisible by 9 or 11. - Obtain the following aralization . The int e nted

Answer 1

176521221 divisible by 9 but not by 11

149235678 divisible by 9 but not by 11

Explanation:

There are rules that can be used to determine if a number is divisible by other. We will use the following:

- A number is divisible by 9, if the sum of its digits is divisible by 9.

- A number is divisible by 11, if the alternating sum of the digits read from left to right is divisible by 9.

Let's apply this rules to the given numbers...

For 176521221:

• 1 + 7 + 6 + 5 + 2 + 1 + 2 + 2 + 1 = 27, and 27 divisible by 9 => 176521221 divisible by 9

• 1 - 7 + 6 - 5 + 2 - 1 + 2 - 2 + 1 = -3, and -3 not divisible by 11 => 176521221 not divisible by 11

For 149235678 :

• 1 + 4 + 9 + 2 + 3 + 5 + 6 + 7 + 8 = 45, and 45 divisible by 9 => 149235678 divisible by 9

• 1 - 4 + 9 - 2 + 3 - 5 + 6 - 7 + 8 = 9, and 9 not divisible by 11 => 149235678 not divisible by 11