Find the total number of integer n such that 2≤n≤2000 and H.C.F. of n and 36 is 1.

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Find the total number of integer $n$ such that $2 \leq n \leq 2000$ and H.C.F. of $n$ and 36 is 1.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 666.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$36 = 3^{3} \times 2^{2}$
No. of numbers between 2 and 2000 divisible by 2 is 1000
No. of numbers between 2 and 2000 divisible by 3 is 666
No. of numbers between 2 and 2000 divisible by 6 is 333
No. of numbers divisible by 2 or 3 is $1000 + 666 - 333 = 1333$
No. of integers that are not divisible by 2 or 3 is $1999 - 1333 = 666$