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.
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.
I had to go through many other videos before stumbling upon your vedio to understand in simple terms Euler’s totient function% thank you very much for explaining to a lay man like me with simple examples in a succinct manner
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.
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?
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.
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.
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.
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.
Write bro
@@editorsam8813 right hota hai
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
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?
@@hossammahmoud6821 he did prime factorization on 369 and 372
thanks
I had to go through many other videos before stumbling upon your vedio to understand in simple terms Euler’s totient function% thank you very much for explaining to a lay man like me with simple examples in a succinct manner
You are one of the best teachers so far. Thanks for this amazing video that explains everything the simplest way.👏👏
= 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.
Answers: 240,120
Sure
My finals will be in a a few hours. Thank you for the clear explanation! :D
Which event were you participating?
Pass or failed?
phi(369) = 2^2*41=240
phi(372)=2^2*3*31=120
thank you for this video ;)
I think there is 3^2*41 =240.
Thank you professor. I understand how to properly use eulers totient function
Sir,
It's my humble request 🙏🏻
Plz add more video in playlist of data structure.
Plz plz🙏🏻🙏🏻🙏🏻🙏🏻
incredible content. lucid explanation. all the best
Thanks bro i learn it,👍..by the way ur answers 240 and 120.
Thanks sir 🙏 ☺️ you explained it in a very easy way 👍 🎉
Great video
very nice explanation sir. continue like this
Excellent lecture
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.
Best explanation I’ve found for this. Thanks!
Answer of homework questions
1. Phi(369)=240
2. Phi(372)=120
Thank you so much sir.
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?
You learn how to factorize a number from youtube then come
you need to study 7th class mathematics again
yo thanks for teaching me this
Excellent lecture
Thanks alot
∅(369) =240
∅(372) =120
😊 thank you creators, always helping me to revise quickly before exams.. ❤
Great movie, however it would have been good to solve bigger number such as phi(33389)
Phi of 369 is 240 and phi of 372 is 120❤️
LIFE SAVER!!!
Thanks sir👍👍
Top class
Thank you so much😊
I love you so much sir
369 = 123 * 3
= 122 * 2
= 244
123 is not a prime no. , so this is wrong
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 😂😂😂
Ans:-Q1-240,Q2-120
Thank u
Sir pi of thousend lo 2,5 prime number so formula wrong sir second formula may substitute
What if the prime numbers p and q are same? How do we calculate?
Solve for phi(25)
is it same as n is prime!
i.e. phi (25)= n-1=25-1=24?
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.
1. 240
2. 120
How to solve phi(25)
Can any body help
Can anyone share the full solution of the homework? I wanna see it
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)
@@PRITESHKRSRV but another 3 is not calculated y please explain me..👀
@@pruthvirajgspruthvi4315 use distinct prime formula discussed in video
11:13 phi(1000) = 40
400 po
Answers are 240 and 120
phi(369) = 240, phi(372) = 120
if i solve phi(1000) according to second formula i was getting 4. note(here 2 and 5 both are prime numbers )
Kid read the second formula again. product of 2 and 5 is not equal to 1000
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
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?
How you people got to know the factors of 369 and 372?
In this cases you have to calculate factors, by dividing starting from 2 and onwards
What about the last formula ?? n=a×b.... Composite...where is s or b in the formula?//
COMPLETELY WRONG FORMULA FOR THE LAST ONE!!
how to find phi of 25
Using the 3rd formula. 25×(1-1/5)=20
240&120
How can we cross check whether ans is correct or not?
Apply Standard method, calculate GCD of each digit and verify. That's all you can
Phi(27)
18
How to find for 761
761 is a prime number so just use 1st formula
761-1 = 760
224; and 330
phi ( 369 ) = 240
phi ( 372 ) = 120
how u got the 1st answer
@@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
@@akarshmalhotra1154 But 3 and 41 both are prime so how it can fall under Case 3??
Pi(369)=60 pi (372)=60
240 n 120
240,120
Phi(25)=20
How by using eulers
@@sathvicendra4108 5^2=25 that's why 25*(4/5)=20
Sir but how would we solve for 25😢😢😢
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.
@user-kf1yq8nv8x but isn't the answer 20?👀
@user-kf1yq8nv8x But isn't the answer 20?
1:13
Can anyone say of n=49, answer
42
bi
❤️
240
120
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.
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
how u got the 1st answer
240 and 120
phi(369) = 240
phi(372) = 120
phi(369) = 240
phi(372) = 120