how many numbers between 1 and 1050 are divisible by 35 or 7

Solution

number of integers divisible by 3 between 1 and 1050 = 349

number of integers divisible by 5 between 1 and 1050 = 209

number of integers divisible by 7 between 1 and 1050 = 150

number of integers divisible by 3 and 5 between 1 and 1050 = 69

number of integers divisible by 3 between 7 and 1050 = 49

number of integers divisible by 5 between 7 and 1050 = 29

number of integers divisible by 3 ,5 and 7 between 1 and 1050 = 9

number of integers divisible by 3,5 or 7 between 1 and 1050 =

349+209+150-69-49-29+9=570

so answer is 570.

note that i have not included 1050.

if you wanna include it then add 1 to the answer.