Maths ·Class 9 Maths

How many three-digit numbers are divisible by 7? Class 9

RBSEGuide

· Jul 10, 2026 · Reviewed & updated Sep 17, 2026 · 1 min read

Question 1.

(Hint: All three-digit numbers divisible by 7 form an AP. Find the smallest and largest such three-digit numbers.)

Solution:

The three-digit numbers divisible by 7 are 105, 112, 119,..., 994

∴ Smallest and largest three-digit number is 105 and 994, respectively.

The list of numbers is an AP with first term a = 105 and common difference

d = 112 - 105 = 7

Let the number of terms of this AP be n.

Then

t_n = 994

∴ a + (n - 1)d = 994

∴ 105 + (n - 1) (7) = 994

∴ 7(n - 1) = 994 - 105

∴ 7(n - 1) = 889

∴ n - 1 = $\frac{889}{7}$ = 127

∴ n = 128

∴ There are 128 three-digit numbers which are divisible by 7.