All Questions
Tagged with prime-factorization factorial
55
questions
5
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6
answers
15k
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Product of r consecutive integers is divisible by r! [duplicate]
Well in a book i am reading it is given that you can also prove this by showing that
Every prime factor is contained in $(n+r)!$ as often at least as it is contained in $n!r!$.
How does this prove ...
- 6,922
7
votes
2
answers
187
views
The number of primes in the factorization of $N!$
Is there an approximation to the number of primes in the factorization of $N!$?
For example:
For $N=10$, this number is $15$.
For $N=100$, this number is $239$.
For $N=1000$, this number is $2877$.
...
- 43.2k
2
votes
3
answers
443
views
Factoring added factorials
How do I facilitate prime factorization without brute-forcing the 600+ digit number?
For example, how would I factor (82! + 83! + 84!) ?
- 99
7
votes
2
answers
7k
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Factorials and Prime Factors
I need to write a program to input a number and output it's factorial in the form:
$4!=(2^3)(3^1)$
$5!=(2^3)(3^1)(5^1)$
I'm now having trouble trying to figure out how could I take a number and get ...
- 71
5
votes
2
answers
191
views
Show that there is no natural number $n$ such that $3^7$ is the largest power of $3$ dividing $n!$
Show that there is no natural number $n$ such that $7$ is the largest power $a$ of $3$ for which $3^a$ divides $n!$
After doing some research, I could not understand how to start or what to do to ...
- 3,789
6
votes
3
answers
129
views
If $N$ is a multiple of $100$, $N!$ ends with $\left(\frac{N}4-1 \right)$ zeroes.
Did certain questions about factorials, and one of them got a reply very interesting that someone told me that it is possible to show that
If $N$ is a multiple of $100$, $N!$ ends with $\left(\frac{...
- 3,789
3
votes
1
answer
94
views
Find the smallest value of $n$ so that the greater potency of $5$ which divides $n!$ is $5^{84}$. What are the other numbers that enjoy this property?
Find the smallest value of $n$ so that the greater potency of $5$ which divides $n!$ is $5^{84}$. What are the other numbers that enjoy this property?
I thought I would put together an equation of ...
- 3,789
8
votes
2
answers
482
views
Find the greatest power of $104$ which divides $10000!$
Find the greatest power of $104$ which divides $10000!$
I thought $$104=2^3\cdot13$$ so I have to find $n$ such that $$(2^3\cdot13)^n\mid 10000!$$ Obviously, we can see that there are fewer factors $...
- 3,789
2
votes
1
answer
2k
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Find the prime factor decomposition of $100!$ and determine how many zeros terminates the representation of that number. [duplicate]
Find the prime factor decomposition of $100!$ and determine how many zeros terminates the representation of that number.
Actually, I know a way to solve this, but even if it is very large and ...
- 3,789
3
votes
2
answers
159
views
A question about prime factorization of $n!$
Prove that for any integer $K$, There exists a natural number $N$ so that in the prime factorization of $N!$ we can find at least $K$ prime numbers which their powers are exactly $1$.
- 4,991