how many three digit numbers are divisible by 5

There are 180 three-digit numbers that are divisible by 5.

Quick Scoop

A three-digit number is divisible by 5 if its last digit is 0 or 5.

So the valid three-digit numbers start at 100 and go up to 995:
100, 105, 110, …, 995.

This forms an arithmetic progression where:

• First term a=100a=100a=100
• Last term l=995l=995l=995
• Common difference d=5d=5d=5

Use the AP formula l=a+(n−1)dl=a+(n-1)dl=a+(n−1)d:

995=100+(n−1)×5995=100+(n-1)\times 5995=100+(n−1)×5

895=(n−1)×5895=(n-1)\times 5895=(n−1)×5

n-1=179 \Rightarrown=180

So, 180 three-digit numbers are divisible by 5.

TL;DR: Among all three-digit numbers from 100 to 999, exactly 180 are multiples of 5.

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