Question

count no. of integers between 1 and 600 inclusive which are not divisible by 6 ​

Answer 1

300 integers

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Answer 2

Answer:

Count no. of integers between 1 and 600 inclusive which are not divisible by 6 ​ is 275

Step-by-step explanation:

Given:

From the numbers between 1 and 600,

Number of numbers divisible by $3=200$

$600=3+(n-1)3$

$= > n=200$

[Arithmetic Progression last term formula->

$l=a +(n-1)d]$

Find: Count no. of integers between 1 and 600

Similarly,

Number of numbers divisible by $5=120$[A.P formula to get number of terms]

Number of numbers divisible by $5 (but not by 3)=80$

Here, we will subtract the numbers divisible by 3 and 5 both i.e. number divisible by 15.

Numbers divisible by 15 in 1 to $600=40$

Number of numbers divisible by 5 (but not by 3)$=120-80=40$

Now, we will calculate the numbers divisible by 7(but not by 3 and 5)=

We will remove the numbers divisible by 3,5 and 15.

Numbers divisible by 7(but not by 3 and 5)=45.

Hence, total number of numbers between 1 and 600 which are not divisible by 3,5 or $7=600-200-80-45$

$=600-325$

$=275$