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Euler’s Totient Function (Solved Examples)

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Network Security: Euler’s Totient Function (Solved Examples)
Topics discussed:
1) Definition of Euler’s Totient Function Ф(n) or Phi Function Phi(n).
2) Explanation on how to find the Ф(n).
3) Solved examples of finding Ф(n) for larger numbers using formulas.
4) Various scenarios of n in Ф(n) such as ‘n’ being prime, ‘n’ being a product of two prime, and ‘n’ is a product of composite-prime-composite combination.
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Опубликовано:

5 сен 2024

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Комментарии : 100

@rajeshprajapati4863 2 года назад

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 2 года назад

Write bro

@omop5922 Год назад

@@editorsam8813 right hota hai

@AkshayKumar-re6kl 2 года назад

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 Год назад

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 Год назад

@@hossammahmoud6821 he did prime factorization on 369 and 372

@amanmotghare7196 5 месяцев назад

thanks

@harshitshukla1974 6 месяцев назад

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.

@amaviamah2274 11 месяцев назад

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

@thanmaijami8962 2 года назад

Answers: 240,120

@Arihantdesai413 8 месяцев назад

Sure

@hellostranger2709 Год назад

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

@Mahi-nz5ct Год назад

Which event were you participating?

@parmarh3898 Год назад

Pass or failed?

@poonamkumari8525 2 года назад

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

@walidmenghour2639 2 года назад

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

@neelamyadav7609 2 года назад

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

@sonikaur2718 26 дней назад

Thanks sir 🙏 ☺️ you explained it in a very easy way 👍 🎉

@manikandan-m. Год назад

= 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.

@roystargamingfreefire7987 Год назад

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

@balajimetla3886 Год назад

very nice explanation sir. continue like this

@hossammahmoud6821 Год назад

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 11 месяцев назад

You learn how to factorize a number from youtube then come

@ashutosh1727 7 месяцев назад

you need to study 7th class mathematics again

@maryliezlgorzal1365 3 месяца назад

Thank you so much sir.

@swarnalatha7892 Год назад

Excellent lecture

@sastenashe_yt8802 2 года назад

Great video

@Valsula69 4 месяца назад

Best explanation I’ve found for this. Thanks!

@aissalaribi7672 4 месяца назад

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

@quratulain4314 Год назад

Excellent lecture Thanks alot

@michikatsu_tsugikuni-c7m 11 месяцев назад

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

@mandelaaa 2 месяца назад

I love you so much sir

@davidwebdeveloper Год назад

369 = 123 * 3 = 122 * 2 = 244

@hardikkumarsingh 6 месяцев назад

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

@thedevourerofgods1686 2 года назад

yo thanks for teaching me this

@priyavats1847 Год назад

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.

@theblueworld1188 Год назад

Thanks sir👍👍

@saritasethi6202 Год назад

Thank you so much😊

@shloksuman8164 Год назад

LIFE SAVER!!!

@amanrawat3248 2 года назад

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 😂😂😂

@trendystatusforyou 10 месяцев назад

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

@karaganilokeswari2301 Год назад

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

@l032radhakulkarni7 10 месяцев назад

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

@rehansekh2164 2 года назад

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

@IT.Diwakar 2 года назад

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

@RichaSingh-sy7hz 2 года назад

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.

@NCS8331 2 месяца назад

How to find for 761

@Mathchemist__ 2 года назад

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

@PRITESHKRSRV Год назад

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 Год назад

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

@adityarai30 Год назад

@@pruthvirajgspruthvi4315 use distinct prime formula discussed in video

@sathvicendra4108 2 года назад

How to solve phi(25) Can any body help

@rashiagrawal7934 2 месяца назад

1. 240 2. 120

@MMNayem-dq4kd 2 года назад

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

@GreatestIndianRailways Год назад

Ans:-Q1-240,Q2-120

@donthusravya2026 2 года назад

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

@sandrabm3224 2 года назад

how u got the 1st answer

@ujjwalgautam7341 Год назад

Answers are 240 and 120

@nitishjha7756 6 месяцев назад

Sir but how would we solve for 25😢😢😢

@Varsha_Thomas 5 месяцев назад

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 4 месяца назад

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

@Varsha_Thomas 4 месяца назад

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

@pulamarasettinaveen2878 2 года назад

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

@PRITESHKRSRV Год назад

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

@user-pu2tg5xu1c 9 месяцев назад

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

@SARPONGBLESSINGABENA 3 месяца назад

240 and 120

@sadinenisushanth887 Год назад

how to find phi of 25

@shrutibiswas1530 9 месяцев назад

Using the 3rd formula. 25×(1-1/5)=20

@annonymous. 2 года назад

11:13 phi(1000) = 40

@renositon4344 2 года назад

400 po

@shrutikadambhare7650 Год назад

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

@subratamandal2924 6 месяцев назад

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

@devpriyashivani1855 Год назад

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 Год назад

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?

@katrinamaeponcio3386 Год назад

224; and 330

@The.Jaynish 2 года назад

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

@PRITESHKRSRV Год назад

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

@iqraibrar7216 Год назад

Phi(27)

@mehedihassanshimul2248 4 месяца назад

@user-pb6nz5of4t Год назад

240,120

@bhagavantulasi5150 Год назад

Can anyone say of n=49, answer

@mehedihassanshimul2248 4 месяца назад

@onyiesther178 8 месяцев назад

1:13

@aryangoel4893 Год назад

240 n 120

@sohagdhali827 2 года назад

Phi(25)=20

@sathvicendra4108 2 года назад

How by using eulers

@sohagdhali827 2 года назад

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

@karthickkarthick1049 2 года назад

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

@janakiisajeev 2 года назад

❤️

@tsunningwah3471 6 месяцев назад

@monicabattacharya6416 2 года назад

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.