How many numbers between 501 and 1200 are not divisible either by 5 or 7?
Answers
Answer:
the numbers are not divisible either by 5 or 7 = 479
Explanation:
We need to find the number of values in the set of numbers from 501 to 1200 which are not divisible by 5 or 7.
The largest multiple of 5 is before 1200 = 239*5 = 1195 and the largest multiple of 7 just smaller than 1200 is 1197 = 171*7
Number start from 501; So, last number divisible by 5 before 501 is 500 = 100*5
and last number divisible by 7 before 501 is497 = 71*7
So, total numbers divisible by 5 between 501 to 1200 = 239 - 100 = 139
total number divisible by 7 between 501 to 1200 = 171 - 71 = 100
So we have 139 numbers divisible by 5 and 100 numbers divisible by 7. But here we have counted the numbers divisible by both 5 & 7 twice.
The largest number divisible of 35 before 501 is 490 = 14*35
and largest number divisible of 35 before of 1200 is 1190 = 34*35
So, total number between 501 to 1200 divisible by 35 = 34-14 = 20
numbers between 501 and 1200 are divisible either by 5 or 7 = 139 + 100 - 20 = 219
the numbers are not divisible either by 5 or 7 = 698 - 219 = 479
That's the final answer.