Mathematics

How many three digit numbers are divisible by 7 ?

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Three digit numbers which are divisible by 7 are 105, 112, ……., 994.

Let there be n terms.

In above series,

a_n = 994, a = 105 and d = 7.

By formula,

⇒ a_n = a + (n - 1)d

⇒ 994 = 105 + (n - 1) × 7

⇒ 994 = 105 + 7(n - 1)

⇒ 994 - 105 = 7(n - 1)

⇒ 889 = 7(n - 1)

⇒ n - 1 = $\dfrac{889}{7}$

⇒ n - 1 = 127

⇒ n = 128.

Hence, there are 128 three digit numbers, which are divisible by 7.

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