There are 180 three-digit natural numbers that are divisible by 5.
Here's a breakdown of how to determine this:
- Understanding the Range: Three-digit numbers range from 100 to 999.
- Divisibility Rule for 5: A number is divisible by 5 if its last digit is either 0 or 5.
- Finding the First and Last Numbers:
- The first 3-digit number divisible by 5 is 100.
- The last 3-digit number divisible by 5 is 995.
- Forming an Arithmetic Sequence: The numbers divisible by 5 form an arithmetic sequence: 100, 105, 110, ... , 995. Here, the common difference is 5.
- Applying the Arithmetic Sequence Formula:
The formula to find the nth term in an arithmetic sequence is an = a1 + (n-1)d,
Where: an is the last term of the series (995 in this case), a1 is the first term (100), d is the difference (5), and n is the number of terms to be found.
So:
995 = 100 + (n-1)5
895 = (n-1)5
179 = n-1
n = 180
Therefore, there are 180 three-digit natural numbers divisible by 5, confirming the statement from the reference.
