How many three digit numbers are divisible by 7

1.	How many three digit numbers are divisible by 7
Answer» Three digit number are100 to 999105,112,119.......994Ans:128 128 By Euclid divisor lemma -:999 / 7= 142*7+5Here999 is a divident 7 is quoent 142 is divisor 5 is reminder So 7 number is 999-5= 994 (You know that higest nois 3 digit is 999 ) 128 The first 3-digit number which is divisible by 7 is 105The last 3-digit number which is divisible by 7 is 994The list of 3-digit numbers divisible by 7 are105, 112, 119,…..994 which forms an A.PConsider a formulaT(n) = a + (n – 1)dWherea = 105d = 7T(n) = 994994 = 105 + (n – 1)7889 = 7n – 77n = 896n = 128∴ There are 128 3-digits number which are divisible by 7

Discussion