The last formula where phi(n) = n * ( 1 - 1/p) * ( 1 - 1/q) * ( 1 -1/r) .... where p,q,r.... are the distinct prime factors of n is applicable to all the cases. So it can be treated as the one and only required formula. PS: thanks for the great content.

369=>41*3*3; phi(369)=>369*(1-1/41)(1-1/3)=240 372=>31*3*2*2; phi(372)=>372*(1-1/31)(1-1/3)(1-1/2)=120

@hossammahmoud6821

Жыл бұрын

how did u know that u must use 3 and 41 for Φ(369)? how did u know that u must use 2, 3 and 31 for Φ(372)? how did u reach there?

@cs1-34devabalamb9

Жыл бұрын

@@hossammahmoud6821 he did prime factorization on 369 and 372

@amanmotghare7196

4 ай бұрын

thanks

Answer to H.W : 1 : Φ(369) = 240 2 : Φ(372) = 120 So, there are 240 and 120 positive integers that are less than 369 and 372 respectively, also relatively prime to 369 and 372 respectively.

@editorsam8813

Жыл бұрын

Write bro

@omop5922

Жыл бұрын

@@editorsam8813 right hota hai

You are one of the best teachers so far. Thanks for this amazing video that explains everything the simplest way.👏👏

very nice explanation sir. continue like this

Excellent lecture

Excellent lecture Thanks alot

Answers: 240,120

@Arihantdesai413

7 ай бұрын

Sure

Thank you so much sir.

Sir, It's my humble request 🙏🏻 Plz add more video in playlist of data structure. Plz plz🙏🏻🙏🏻🙏🏻🙏🏻

Great video

Thank you so much😊

yo thanks for teaching me this

My finals will be in a a few hours. Thank you for the clear explanation! :D

@Mahi-nz5ct

Жыл бұрын

Which event were you participating?

@parmarh3898

Жыл бұрын

Pass or failed?

Thanks sir👍👍

= phi(3 * 123) = phi (3² * 41¹) ; = 369 * (1 - 1/3) * (1 - 1/41) ; = 369 * 2/3 * 40/41; = 3 * 80 = 240; Thus, 240 numbers are the positive integers that are relatively prime which is less than the given, 369; = Phi(3 * 124) = phi(3 * 31 * 2²) ; = 372 * (1 - 1/3) (1 - 1/31) (1 - 1/2) ; = 372 * 2/3 * 30/31 * 1/2; = 12/6 * 60 = 120; Therefore, 120 positive numbers are relatively prime and lesser than the given, 372.

Thanks bro i learn it,👍..by the way ur answers 240 and 120.

Best explanation I’ve found for this. Thanks!

phi(369) = 2^2*41=240 phi(372)=2^2*3*31=120 thank you for this video ;)

@neelamyadav7609

2 жыл бұрын

I think there is 3^2*41 =240.

I love you so much sir

LIFE SAVER!!!

What if the prime numbers p and q are same? How do we calculate?

Sir pi of thousend lo 2,5 prime number so formula wrong sir second formula may substitute

for the solution of the homwork how did u know that u must use 3 and 41 for Φ(369)? how did u know that u must use 2, 3 and 31 for Φ(372)? how did u reach there?

@rnboy0

10 ай бұрын

You learn how to factorize a number from youtube then come

@ashutosh1727

6 ай бұрын

you need to study 7th class mathematics again

Great movie, however it would have been good to solve bigger number such as phi(33389)

The answer is (i) 240 ,there are 240 number less than 369 that are relatively prime to 369. (ii) 120 , there are 120 numbers less than 372 that are relatively prime to 372.

Thank you thank you thank soo much sir. .i want to touch your feet .. seriously i wasted 2 hour in internet for just learning this thing 😂😂😂

How to find for 761

Answer of homework questions 1. Phi(369)=240 2. Phi(372)=120

Solve for phi(25) is it same as n is prime! i.e. phi (25)= n-1=25-1=24?

@RichaSingh-sy7hz

2 жыл бұрын

But 25 is not a prime number. I think as it is 5^2, so we we take n=5. phi(5)=n-1, n=4.

Phi of 369 is 240 and phi of 372 is 120❤️

Ans:-Q1-240,Q2-120

phi(369)=240 phi(372)=120

How to solve phi(25) Can any body help

Can anyone share the full solution of the homework? I wanna see it

@PRITESHKRSRV

Жыл бұрын

369 = 3^2 X 41 Distinct primes = 3,41 phi(368) = 369 X (1-1/3) X (1-1/41) = 369 X 2/3 X 40/41 = 240 Same Approach for phi(372)

@pruthvirajgspruthvi4315

Жыл бұрын

@@PRITESHKRSRV but another 3 is not calculated y please explain me..👀

@adityarai30

Жыл бұрын

@@pruthvirajgspruthvi4315 use distinct prime formula discussed in video

if i solve phi(1000) according to second formula i was getting 4. note(here 2 and 5 both are prime numbers )

@PRITESHKRSRV

Жыл бұрын

Kid read the second formula again. product of 2 and 5 is not equal to 1000

∅(369) =240 ∅(372) =120 😊 thank you creators, always helping me to revise quickly before exams.. ❤

How can we cross check whether ans is correct or not?

@PRITESHKRSRV

Жыл бұрын

Apply Standard method, calculate GCD of each digit and verify. That's all you can

Answers are 240 and 120

1. 240 2. 120

240&120

how to find phi of 25

@shrutibiswas1530

8 ай бұрын

Using the 3rd formula. 25×(1-1/5)=20

phi(369)=240 , phi(372)=120

@sandrabm3224

2 жыл бұрын

how u got the 1st answer

❤️

Can anyone say of n=49, answer

@mehedihassanshimul2248

3 ай бұрын

42

369 = 123 * 3 = 122 * 2 = 244

@hardikkumarsingh

5 ай бұрын

123 is not a prime no. , so this is wrong

How you people got to know the factors of 369 and 372?

@subratamandal2924

4 ай бұрын

In this cases you have to calculate factors, by dividing starting from 2 and onwards

240 and 120

11:13 phi(1000) = 40

@renositon4344

2 жыл бұрын

400 po

224; and 330

240,120

Phi(27)

@mehedihassanshimul2248

3 ай бұрын

18

240 n 120

Sir but how would we solve for 25😢😢😢

@Varsha_Thomas

4 ай бұрын

Use the third formula. n*(1-1/p) = 25*(1-1/5) = 25*⅘ = 20 The second formula is not possible. We know that 25 = 5*5, however here p and q are NOT distinct. They should be distinct in order to use the second formula.

@Varsha_Thomas

3 ай бұрын

​@user-kf1yq8nv8x but isn't the answer 20?👀

@Varsha_Thomas

3 ай бұрын

@user-kf1yq8nv8x But isn't the answer 20?

1:13

1. Φ(369) = 240 Prime Factors of 369 = [3 * 3 * 41] = [3^2 *41] Φ(369) = 3 * 3 * 41 * (1-1/3) * (1-1/41) = 3 * 3 * 41 * 2/3 * 40/41 = 3 * 2 * 40 = 240 2. Φ(372) = 120 Prime Factors of 372 = [2 * 2 * 3 * 31] = [2^2 * 3 * 31] Φ(372) = 2 * 2 * 3 * 31 * (1-1/2) * (1-1/3) * (1-1/31) = 2 * 2 * 3 * 31 * 1/2 * 2/3 * 30/31 = 2 * 1 * 2 * 30 = 120

@hossammahmoud6821

Жыл бұрын

how did u know that u must use 3 and 41 for Φ(369)? how did u know that u must use 2, 3 and 31 for Φ(372)? how did u reach there?

Phi(25)=20

@sathvicendra4108

2 жыл бұрын

How by using eulers

@sohagdhali827

2 жыл бұрын

@@sathvicendra4108 5^2=25 that's why 25*(4/5)=20

bi

What about the last formula ?? n=a×b.... Composite...where is s or b in the formula?// COMPLETELY WRONG FORMULA FOR THE LAST ONE!!

Pi(369)=60 pi (372)=60

Please start teaching FULL STACK DEVELOPMENT COURSE. I am learning now 😌. if you start it now , it will be helpful for many students who are preparing for placements.

@Umar-nl3ny

2 жыл бұрын

you are everywhere asking for something, pls take it easy on him and yourself

phi(369) = 240 phi(372) = 120

phi(369) = 240, phi(372) = 120

phi ( 369 ) = 240 phi ( 372 ) = 120

@sandrabm3224

2 жыл бұрын

how u got the 1st answer

@akarshmalhotra1154

2 жыл бұрын

@@sandrabm3224 factors of 369 are 3,41 . One of the factors are composite which means Case 3 is applicable i.e 369 * (1-1/3) * (1-1/41) = 240

@navinsingh2784

2 жыл бұрын

@@akarshmalhotra1154 But 3 and 41 both are prime so how it can fall under Case 3??

phi(369) = 240 phi(372) = 120