Among first 500 positive integers
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Determine the integer that are not divisible by 2 ,nor by 3 and nor by 5
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Determine the integers which are exactly divisible by one of them
Answers
Answer:
66
Step-by-step explanation:
First of all, We have to find Total number of integers between 1 and 500 divisible by 3
Multiple of 3 between 1 and 500
3,6,9,12...,498
As we xan see it is an A.P. with common difference 3.
From the last term of the above A.P. we can find total number of terms.
=> 498= 3+(n-1)3
=>495=(n-1)3
=>495/3 = n-1
=>166 = n
But in these terms we have integers which are divisible by 5 and 6.
Now ,we will subtract all the terms which are divisible by 5 and 6
All the multiple divisible by 3 and 6
6, 12,18,...498
Common difference = 6
Using above method of finding the total number of terms,I have
=> 498 = 6+(m-1)6
=>492/6 = m-1
=>n = 83
Now, all those multiple which are divisible by 3 and 5 by not by 6
15,45,75,...,495
Common difference = 30
Total number of terms
=>495 = 15 + (p-1)30
=>480/30 =p-1
=>17 = p.
Therefore,
Total number of terms between 1 and 500 which are divisible by 3 but not by 5 and 6 is given by n-m-p
i.e. 166-83-17 = 66