Legendre's formula finds the exponent of the largest power of some prime p that divides (is a factor of) the factorial of some number n. Legendre's formula example (p = 2 and n = 27): e₂ (27!) To illustrate: 27 27 =]+[]+? =13 +6+3+1 =23 p = 5 n = 100 2 So 2^23 is the largest power of 2 that divides 27!. The formula returns the sum of many fractions (rounded down) with n as the numerator and a steadily increasing power of p as the denominator, stopping when it exceeds the numerator. 27 int(100/5)+ int(100/25) // No 100/125 because 125 > 100. 23
Legendre's formula finds the exponent of the largest power of some prime p that divides (is a factor of) the factorial of some number n. Legendre's formula example (p = 2 and n = 27): e₂ (27!) To illustrate: 27 27 =]+[]+? =13 +6+3+1 =23 p = 5 n = 100 2 So 2^23 is the largest power of 2 that divides 27!. The formula returns the sum of many fractions (rounded down) with n as the numerator and a steadily increasing power of p as the denominator, stopping when it exceeds the numerator. 27 int(100/5)+ int(100/25) // No 100/125 because 125 > 100. 23
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![Legendre's formula finds the exponent of the largest power of some
prime p that divides (is a factor of) the factorial of some number n
Legendre's formula example (p = 2 and n = 27):
€₂ (27!)
To illustrate:
27
27
[]+[] +
2
p = 5
n = 100
=13 +6+3+1
=23
So 2^23 is the largest power of 2 that divides 27!.
The formula returns the sum of many fractions (rounded down) with
n as the numerator and a steadily increasing power of p as the
denominator, stopping when it exceeds the numerator.
27
23
int(100/5)
int(100/25)
// No 100/125 because 125 > 100.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb18782d8-11c0-4e46-a98e-9ff7123396f6%2Fdf338bf3-b239-451e-a60a-8603666312e6%2Fvk2v4xr_processed.png&w=3840&q=75)
Transcribed Image Text:Legendre's formula finds the exponent of the largest power of some
prime p that divides (is a factor of) the factorial of some number n
Legendre's formula example (p = 2 and n = 27):
€₂ (27!)
To illustrate:
27
27
[]+[] +
2
p = 5
n = 100
=13 +6+3+1
=23
So 2^23 is the largest power of 2 that divides 27!.
The formula returns the sum of many fractions (rounded down) with
n as the numerator and a steadily increasing power of p as the
denominator, stopping when it exceeds the numerator.
27
23
int(100/5)
int(100/25)
// No 100/125 because 125 > 100.
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