Q. 64.2( 5 Votes )

How many three - digit natural numbers are divisible by 7?

Answer :

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

This forms an AP with first term a = 105


and common difference = d = 7


Last term is 994.


Now, number of terms in this AP are given as:


994 = a + (n - 1)d


994 = 105 + (n - 1)7


994 - 105 = 7n - 7


889 + 7 = 7n


896 = 7n


n = 128


Therefore 994 is the 128th term in the AP.


There are 128 three - digit natural numbers that are divisible by 7.


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