All Questions
Tagged with prime-factorization factorial
55
questions
0
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67
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Is the sequence infinite? Finite? Is there a general formula to determine n th term?
Sequence of numbers whose factorial on prime factorisation contains prime powers of prime numbers, whose power is greater than $1$ or contains multiplicity of one for all prime numbers less than equal ...
1
vote
2
answers
86
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To determine multiplicity of $2$ in $n!$ [duplicate]
Is there a general formula for determining multiplicity of $2$ in $n!\;?$
I was working on a Sequence containing subsequences of 0,1. 0 is meant for even quotient, 1 for odd quotient.
Start with k=3,...
3
votes
1
answer
76
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Are there infinitely many composiphiles?
I came up with this today: we say a positive integer $k$ is a composiphile if there exists no positive integer $n \leq k$ such that
$$\frac{k!}{n} + 1 \text{ is prime.}$$
My question: are there ...
58
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2
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Can I search for factors of $\ (11!)!+11!+1\ $ efficiently?
Is the number $$(11!)!+11!+1$$ a prime number ?
I do not expect that a probable-prime-test is feasible, but if someone actually wants to let it run, this would of course be very nice. The main hope ...
- 85.1k
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45
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Number dividing the factorial of a lowest prime
I would like to ask a probably simple question but I am not sure how to make it rigorous.
Let $p$ be a prime and $n$ a natural number whose lowest prime factor is $p$. If a natural number $x$ divides ...
- 727
1
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3
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356
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Power of prime in prime factorization of a factorial.
Please advise on how to arrive at solution for determining the power of 17 in the prime factorization of 2890!
Also, is there a short-cut?
So far I know:
Prime factorization of 2890 = 2 x 5 x 17^2
...
- 131
3
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1
answer
126
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The proof of $(n+1)!(n+2)!$ divides $(2n+2)!$ for any positive integer $n$
Does $(n+1)!(n+2)!$ divide $(2n+2)!$ for any positive integer $n$?
I tried to prove this when I was trying to prove the fact that ${P_n}^4$ divides $P_{2n}$ where $n$ is a positive integer, where $P_{...
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2
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Prime Factorization of very big factorials [duplicate]
Is there a quick way to prime factorize 50!.
I wrote down all the numbers and then factorized, but that takes way too long.
-1
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4
answers
1k
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Last non zero digit in 20! [duplicate]
So I have a question where it says to find the last non zero digit of $20!$
I proceeded in the following way:
Found the prime factorization of $20!$ by calculation the greatest powers of $2,3,5,7,11,...
- 1,454
2
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0
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35
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Proof Involving Factors Of Arbitrarily Large Numbers [duplicate]
For prime $p$, show whether $$\prod_{p \geq 1} p^{\lfloor \frac{x}{p-1} \rfloor} \sim x!$$ as $x$ approaches infinity, and
explain.
I don’t know that it’s true, but I thought that it followed, if ...
- 1,789
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2
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367
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Logarithm of factorial equal to sum of logarithm of primes
Let $N$ a positive integer. Denote $\mathcal{P}$ the set of prime numbers. I have to show that
\begin{align}
\log(N!) = \sum_{p^{\nu}\leq N \\ p\in \mathcal{P}} \left\lfloor\dfrac{N}{p^{\nu}}\right\...
- 866
4
votes
1
answer
79
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Solution of $n!=p+1 $ with $p$ is prime number?
One of my friend asked me to solve this equation $n!=p+1 $ with $p$ is prime number and n is positive integer , it's clear that for $p=2$ there is no solutions because : $n! < 3$ for $n=1$ , But ...
- 7,195
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3
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Find the number of trailing zeros in 50! [duplicate]
My attempt:
50! = 50 * 49 *48 ....
Even * even = even number
Even * odd = even number
odd * odd = odd number
25 evens and 25 odds
Atleast 26 of the numbers will lead to an even ...
- 321
3
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0
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47
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How to find the prime factorization of a very large number. [duplicate]
I want to know if there are any tricks or shortcuts to write the factorial of a large number, like $20!,$ as the product of its prime factors.
For example, $5!= 5 \times 3 \times 2^3$
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6
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Find smallest positive integer $n$ such that $n!$ is divisible by $p^k$ ($p =$ positive prime, $k =$ positive integer)
I have to find smallest positive integer $n$ in such way that $n!$ is divisible by $p^k$ ($p$ is always positive prime and $k$ is always positive integer).
$p$ and $k$ are given, $n$ is (obviously ...
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