How many three-digit numbers are divisible by 7?

By Shivank Goel|Updated : August 4th, 2022

We should find the number of three-digit numbers which are divisible by 7

The nth term of AP is aₙ = a + (n - 1)d

Where

aₙ is the nth term,

a is the first term,

d is a common difference,

n is the number of terms

First three-digit number divisible by 7 = 105

Next number = 105 + 7 = 112

So the series is 105, 112, 119, ...

It forms an AP with 105 as the first term, and 7 is the common difference

If we divide 999 by 7, 5 will be the remainder

999 - 5 = 994 is the maximum possible three-digit number, which is divisible by 7

So the final sequence is 105, 112, 119, .... 994

the nth term of an AP = 994

a = 105

d = 7

aₙ = 994

We should find n

nth term of an A.P. is aₙ = a + (n - 1)d

994 = 105 + (n - 1)7

889 = (n - 1)7

n - 1 = 889/7

n - 1 = 127

n = 127 + 1

n = 128

Therefore, when asked How many three-digit numbers are divisible by 7? then the answer will be 128 three-digit numbers are divisible by 7.

Summary:

How many three-digit numbers are divisible by 7?

128 three-digit numbers are divisible by 7.

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