How many of the smallest 200 positive integers are divisible by 3,5, and/or 7?

To Find :

How many of the smallest 200 positive integers are divisible by 3,5 and 7 .

Solution :

We have to find number which are divisible by all 3,5 and 7 .

So , we will find numbers which are divisible by their H.C.F .

Since , 3 ,5 and 7 are prime numbers .

Therefore , their H.C.F is .

Now , we can see that HCF is 105 , so the next number which is divisible by all of them are which is greater than 200 .

Therefore , their is only 1 number i.e 105 less than 200 which is divisible by 3,5 and 7 .

Hence , this is the required solution .

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: