# Numbers divisible by 3

## Homework Statement

How many 3 digit numbers are divisibIe by 5?

## The Attempt at a Solution

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Attempt to a solution?

I don't get 136. How did you come up with that answer?

Defennder
Homework Helper
I don't get 136 either. How did you get that?

Dick
Homework Helper
There are 'roughly' 20 numbers in every 100 that are divisible by 5. There are 'roughly' 900 three digit numbers. So there are 'roughly' 180 three digit numbers divisible by 5. That's enough off from 136 to make me agree with Defennder and Tedjin. You must be wrong.

5, 10, 15, 20, 25, 30

Its all the numbers that end in 5 or zero, and then ignore the last one (1000) because it had the temerity to posses 4 digits.

As you start building the sequence, you see the rule easy enough.

an=nth term of an AP (Arithmetic progression)
a=1st term
d=common difference

Since the 1st 3 digit no. divisible by 5 is 100
a=100
the last 3 digit no. divisible by 5 is 995
an=995
common difference (d)=5
n=no. of 3 digit nos. divisible by 5

an=a+(n-1)d
995=100+(n-1)5
995-100=(n-1)5
895=(n-1)5
895/5=n-1
179=n-1
179+1=n
n=180

Therefore,
exactly (not roughly) 180 3 digit numbers are divisibe by 5

Absolutely correct Dick!!!

@Amith2006
How did you get 136?! Last edited:
Borek
Mentor
Year that passed since the thread was started was enough to count these numbers using fingers.

Aha that made me laugh, insane bump