How Many 3-Digit Numbers are Divisible by 3

Introduction

We will start off with a few definitions for the clearance. A number which has three digits in them is known as a three-digit number. The range is from 100 to 999. Thus, there are a total of 900 3-digit numbers. Likewise, a 3-digit number is divisible by 3 if you divide the three-digit number by ‘3’ and you obtain a whole number with no remainder. Below you will find multiple questions and answers related to three-digit numbers that are divisible by 3.

Three Digit Numerals That are Divisible by 3

Below is a list of all the 3-digit numbers divisible by 3 in increasing order. There are 300 three-digit numerals that are divisible by 3.

102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150,…......,954, 957, 960, 963, 966, 969, 972, 975, 978, 981, 984, 987, 990, 993, 996, 999

The sequence is in arithmetic progression (A.P.) with a standard difference of 3.

Therefore, the number of terms, n during this sequence is the number of three-digit numbers that are divisible by 3.

Using the formula:

last term = 1st term + (n-1)* common difference, we have:

999 = 102 + (n-1)*3

(999–102)/3 = (n -1)

897/3 = 299 = n -1

Therefore,

n = 299 + 1 = 300

Therefore, the number of three-digit numbers divisible by 3 is 300.

Three-digit numerals that are not divisible by 3

Like the above, there are a total of 900 three-digit numbers and 300 of them are divisible by 3.

Likewise, 900 - 300 = 600. Therefore, the three-digit numbers which are not divisible by 3 are 600.

The sum of all 3 digit numerals that are divisible by 3

We summed up all the 3-digit numbers in our list above. The total sum of all three-digit numbers divisible by 3 is 165150.

3-digit numbers that are the smallest and are divisible by 3

The lowest or smallest 3-digit number divisible by 3 is the first number on the list above that is 102.

3-digit numbers that are the largest and are divisible by 3

The greatest or largest 3-digit number divisible by 3 is the last number on the list above, which is 999.

Summary

There are 300 three-digit numbers that are divisible by 3 from 102, 105, 108,......,993, 996, and 999.