How Many Three-digit Number are Divisible by 7?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Do you know how many 3-digit numbers are divisible by 7? The answer is 128. But how did we find that out? To find out how many three-digit number are divisible by 7, we must go through the following steps.

Step 1 – Identify that the given sequence is an AP or arithmetic progression

Step 2 – Find out the number of terms in the given AP

Scroll down to find out how to calculate and find out how many three-digit numbers are divisible by 7.

Table of content

1. 128 three-digit numbers are divisible by 7
2. How Many Three-digit Number are Divisible by 7?

Answer:

128 three-digit numbers are divisible by 7

Now, let’s find out how we can reach this answer by following the abovementioned steps.

So, the first 3-digit number divisible by 7 is 105, and the last 3-digit divisible by 7 is 994.

Hence, the sequence of numbers will be something like 105, 112,_____, 994. As you can see, this is an arithmetic progression with a difference of 7 between the numbers.

Now, to find the number of terms in the AP:

The nth term of an AP is given by: an=a+(n−1)d

Here, A is the first term, and n is the term

Also, d is the common difference between the terms

So, an−>nth term

Hence, a= 105, an= 994 and d= 7

994 = 105 + (n-1)7

889 = 7n – 7

7n = 896

n = 128

Hence, we can say that 7 is divisible by 128 three digit numbers

Summary: