Thread: algebra

State Whether Each Number Below Is Divisible By 2,3,5,9,10 Or None.
Some Numbers May Have More Than One Divisor.

111

288

52

4805

Originally Posted by ricky j

State Whether Each Number Below Is Divisible By 2,3,5,9,10 Or None.
Some Numbers May Have More Than One Divisor.

111

288

52

4805

This is a good exercise in division. Is there a specific problem you are having that we can help you with? Otherwise, just divide by each possible divisor and you have your answer. For example:
111 is divisible only by 3

288 is divisible by 2, 3, and 9.

I'll let you work out the last two.

-Dan

Hello, Ricky!

State whether each number below is divisible by 2,3,5,9, or 10, or None.

(a) 111 . . (b) 288 . . (c) 52 . . (d) 4805

What's stopping you?
Don't you have a calculator . . . or a pencil?


Okay, they must expect you to know some Divisibility Tests
. . so you can simply "eyeball" the numbers.
You already know some of them . . . right?

. . A number is divisible by 2 if it is even (its last digit is even).
. . A number is divisible by 3 if the sum of its digits is divisible by 3.
. . A number is divisible by 5 if it ends in 0 or 5.
. . A number is divisible by 9 if the sum of its digits is divisible by 9.
. . A number is divisible by 10 if it ends in 0.


(a) 111

It ends in "1", an odd number . . . not divisible by 2.

The sum of its digits is: .1 + 1 + 1 = 3, which is divisible by 3.
. . Hence, 111 is divisible by 3.

The last digit is not 0 or 5 . . . not divisible by 5 or 10.

The sum of its digits is 3, which is not divisible by 9.

. . Therefore, 111 is divisible by 3 (only).


(b) 288

It ends in "8", an even number . . . divisible by 2.

The sum of its digits is 2 + 8 + 8 = 18 . . . divisible by 3 and by 9.
. . Hence, 288 is divisible by 3 and 9.

It does not end in 0 or 5 . . . not divisible by 5 or 10.

. . Therefore, 288 is divisible by 2, 3, and 9.


Got it?