CLEAR
Toprankers-Info

+91 7676564400

Mobile App

Get it on Google Play
Discussions
Tags:

Articles

Discussions
Submit Discussion
Varsha Sekar

· started a discussion

· 1 Months ago

Find the number of positive integers less than 3600 that are co-prime to 3600. (Question:948120.0)

Please explain

Question:
Find the no of positive integers less or equal to 3600 which are prime to 3600
Options:
A)

480 

B)

960

C)

1440 

D)

1800  

E)

1600  

Solution:

Ans: (b)

360036 × 1004 × 9 × 4 × 25 = 24 × 32 × 52

When N = ap × bq × cr ×. . . . where a, b, c, . . . are primes,.

 the number of natural numbers less than N, that are co-prime to N is given by

ϕN=1-1a1-1b1-1c    ……..

Here N = 3600 = 21 × 32 × 52

∴ϕN=36001-121-131-15    

=3600×12×23×45=960    

 Alternate sol.:

Factors of 3600 are 2,3,5

total numbers = 3600
numbers multiples of 2 = 1800 -ve
numbers multiples of 3 = 1200 -ve
numbers multiples of 5 = 720 -ve
numbers multiples of 6 = 600 +ve
numbers multiples of 15 = 240 +ve
numbers multiples of 10 = 360 +ve
numbers multiples of 30 = 120 -ve

Hence remaining no. are 960

Knowledge Expert

· commented

· 1 Months ago

Dear student,
Given answer is correct, please read the solution.
Keep learning,
Team TR
-logo
We at aim to provide most comprehensive content & test for practice which is carefully divided into various chapters and topics to help you focus on your weak areas.Our Practice mock test gives you unmatched analytics to help you realize your strong areas,time management and improvement areas.Our Short & Crisp notes on each topic will help you to quickly revise the topic along with the tips & tricks of the exams.
More About
-Info
-Info

Mobile App

Get it on Google Play
About Us Campus Ambassador Careers Contact Us Refund Policy

All Rights Reserved Top Rankers

User Policy
Disclaimer
Terms & Conditions