Question

How many integers between 1 to 500 are NOT divisible by 3 or 4 or 5 or 6.

Answer 1

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

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