Q. 134.2( 193 Votes )

How many three-digit numbers are divisible by 7?

Answer :

Since, 100 is the smallest three digit number and it gives a reminder of 2 when divided by 7, therefore, 105 is the smallest three digit number which is divisible by 7


Since, 999 is greatest three digit number, and it gives a remainder of 5, thus 999 – 5 = 994 will be the greatest three digit number which is divisible by 7


Therefore, here we have,


First term (a) = 105,


The last term (an) = 994


The common difference = 7


We know that, an = a + (n – 1)d


Or, 994 = 105 + (n – 1)7


Or, (n – 1)7 = 994 – 105 = 889


Or, n – 1 = 127


Or, n = 128


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

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