All Questions
Tagged with prime-factorization algebra-precalculus
28
questions
2
votes
2
answers
144
views
Finding positive integer $n>10$ that maximizes $\frac{\sigma_0(n)}{2^{\log n}}$
Among all the positive integer, which one integer, $n$, can make the number below the largest?
$$f(n)=\frac{\sigma_0(n)}{2^t}$$where $t=\log_{10}n$ and $\sigma_0$ is the divisor function.
For example,...
- 183
2
votes
1
answer
77
views
What are the other factors of x if we know 2, 4, and 9 are factors. [closed]
The factors of x include 2, 4, 9. Which of the following are also factors of x?
{1, 3, 5, 6, 8, 10, 12, 18, 24, 36}
Apparently the correct answer is {1, 3, 6, 12, 18, and 36} but I have trouble seeing ...
- 31
0
votes
4
answers
111
views
Show that there are infinitely many functions $f:\mathbb N\rightarrow\mathbb N$ satisfying $f(2)=2$ and$f(mn)=f(m)f(n) \forall m,n\in \mathbb N$
Show that there are infinitely many functions $f:\mathbb N \rightarrow \mathbb N$ such that
(a) $f(2)=2$
(b) $f(mn)=f(m)f(n)$ for all $m,n\in \mathbb N$$
Solution as in book:
Here we use another ...
- 3,835
-1
votes
2
answers
97
views
Factoring- Pre Algebra Homework question
I'm studying pre-algebra with an App called Brilliant. I'm in a lesson called "Factoring Sums with Variables". I got most of the exercises right, but there's one that I don't understand. To ...
- 101
0
votes
0
answers
85
views
Can single variables be called prime factors?
Prime factor decomposition of a term like 10y²z³ gives some prime numbers and single variables, e.g., 2×5×y×y×z×z×z. In this example, 2 and 5 can be called prime factors, can't they? Can y and z be ...
- 123
1
vote
1
answer
164
views
If $PQRSPQRS$ is an eight-digit number with $56$ divisors, find the number of divisors of $PQRS$.
$PQRS$ is a four-digit number where $P,Q,R,S$ are the digits of the number. If $PQRSPQRS$ is an eight-digit number with $56$ divisors (including $1$ and $PQRSPQRS$), find the number of divisors of $...
- 8,318
2
votes
1
answer
59
views
How to find the number of compound divisors of the smallest product from two unknown numbers?
The problem is as follows:
The number of panadol pills at a pharmacy is a positive whole number
that it has two prime divisors and 45 positive divisors. The number of
tylenol pills at the same ...
- 4,185
1
vote
1
answer
127
views
A Question About Euler's Factorization Method
I'm trying to understand Euler's factorization method from this article: https://en.wikipedia.org/wiki/Euler%27s_factorization_method. What I don't understand is when the article states "As each ...
- 31
0
votes
1
answer
74
views
Upper Bound and Lower Bound of the Sum of the Prime Divisors of a Odd Semiprime
Lets say we have $n$, an odd semiprime. $p$ and $q$ are odd primes, such that $pq=n$. What are the tightest upper and lower bounds of $p+q$ in terms of $n$ known right now? Right now, I have $2\sqrt n\...
- 788
1
vote
3
answers
2k
views
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
2
votes
3
answers
766
views
Find the prime factors of $3^{32}-2^{32}$
I'm having a go at BMO 2006/7 Q1 which states: "Find four prime numbers less than 100 which are factors of $3^{32}-2^{32}$."
My working is as follows (basically just follows difference of two squares ...
- 305
1
vote
2
answers
286
views
Relatively prime factors of $24500$
Let $N=24500$, then find the number of ways by which $N$ can be resolved into two coprime factors?
My tries:
$N=24500=2^2\cdot 5^3\cdot 7^2$, for co prime no those two factors of $24500$ should ...
- 1,943
1
vote
4
answers
97
views
When $f(x)=\frac{-b^2m-ba+ax}{-mx-bm-a}$ is an integer
$a,b,m,x$ are positive integers.
For which $x>0$ is $f(x)$ an integer?
$$f(x)=\frac{-b^2m-ba+ax}{-mx-bm-a}$$
I been trying to play with it, I changed it to:
$$\frac{b^2m-a\left(b+x\right)}{a+m\...
- 1,460
1
vote
1
answer
73
views
When $f(x) = \frac{ax + b}{a -x + 1}$ is an integer
Given that $a$ and $b$ are positive integers. and $$f(x) = \frac{ax + b}{a -x + 1}$$ is an integer, what integer values can x have?
If I could only somehow move $x$ from numerator to the denominator ...
- 1,460
-1
votes
1
answer
87
views
How to factorize the expression $4(ab+cd)^2-\left(a^2+b^2-c^2-d^2\right)^2$? [closed]
Factorise$$4(ab+cd)^2-\left(a^2+b^2-c^2-d^2\right)^2$$
I can't solve this math assignment from my text book. No one knows how to solve it, so I would be so thankful to you if you presented your step-...
- 11