24 Answered Questions for the topic Prime Factorization

Can one factor matrices?

I know that one can factor integers as a product of prime numbers. Is there an analog of it to matrices? Can we define prime matrices such that every matrix is a product of prime matrices? Is there... more

Negative factors of a number?

Can a factor of a number be negative? Is -5 a factor of 25 or -25? A number is said to be prime if it has two factors : 1 and the number itself. So if -5 can be a factor of 5, how to define the... more

fastest method to determine if two numbers are coprime?

I am working on a mathematical problem that involves coprime integers. I wrote a computer program that allows me to search for the numbers I am looking for. However I am looking at a large set of... more

Are all highly composite numbers even?

A highly composite number is a positive integer with more divisors than any smaller positive integer. Are all highly composite numbers even (excluding 1 of course)? I can't find anything about this... more

Numbers that are the sum of the squares of their prime factors?

A number which is equal to the sum of the squares of its prime factors with multiplicity: - $16=2^2+2^2+2^2+2^2$ - $27=3^2+3^2+3^2$ Are these the only two such numbers to exist? There has to be... more

Can it be proven/disproven that there are highly composite numbers that prime-factorize into larger primes such as $9999991$?

Of course, following the rules found by Ramanujan, such a highly composite number would need to factorize into all primes ascending up to 9999991 (with descending powers as the primes progress) so... more

When is $4n^4+1$ prime?

Find all natural numbers $n$ such that $4n^4+1$ is prime. $4n^4+1$ is obviously prime when $n=1$. But can we prove that no other $n$ works?

Find $C$ such that $x^2 - 47x - C = 0$ has integer roots, and further conditions?

Have been working on this for years. Need a system which proves that there exists a number $C$ which has certain properties. I will give a specific example, but am looking for a system which could... more

Greatest prime factor of $4^{17}-2^{28}$?

I have seen the solution to this problem. > What is the greatest prime factor of $ \\ 4^{17} - 2^{28} \\ $? Answer: 7 $$ 4^{17}-2^{28} \\ = \\ 2^{34}-2^{28} \\ = \\ 2^{28} \\ (2^6-1) \\ = \\... more

How many primes do I need to check to confirm that an integer $L$, is prime?

I recently saw the 1998 horror movie "Cube", in which a character claims it is humanly impossible to determine, by hand without a computer, if large (in the movie 3-digit) integers are prime... more

Find a prime factor of $7999973$ without a calculator?

How would you go about finding prime factors of a number like $7999973$? I have trivial knowledge about divisor-searching algorithms.

Prime factorization of 5005 if each digit increases from left to right what is the code

Brent knows that the 6-digit number he uses to open his computer is the prime factorization of 5005. If each dodger of the code increases from left to right, what is his code?

Maritza remembers her PIN because it is between 1000 and 1500 and it is the product of two consecutive prime numbers. What is her PIN

Marie remembers her PIN because it is between 1000 and 1500 and it is the product of two consecutive prime numbers. What is her PIN?  

A three digit number has the same hundreds, tens, and ones digits. The sum of the prime factors of the number is 47. What is the three digit number?

This problem is regarding using the prime factorization of numbers.  Can get the right answer but need and explanation of how to begin this process and take it through till the end.

write all the composite numbers less than or equal to 50 in prime factoriation

Another prime problem! Help me please!

Prime factorization of a rectangular board

a recantgular board measures 126cm by 90 cm.  the game board is divided into small squares of equal size.  find the longest possible length of the side of one of the small squares.

A rectangle game board measures 126 cm by 90 cm. The game board is divided into small squares of equal size.

Find the longest possible length of the side of one of the small squares.  And find the least number of squares the game board can be equally divided into.

The 6 digit number is prime factorization of 5005. If each digit of those increases from left to right, what is his code?

Brent knows that the 6 digit number he uses to open his computer is the prime factorization of 5005. If each digit of those increases from left to right, what is his code?

what must subtract from 99 to make it a perfect square

what must subtract from 99 to make it a perfect square by prime factorization method  

I dont understand the question. Can you explain?

At 10am an airplane departs from hanger A, Hanger b, and hanger c. Airplanes depart from Hanger A every 15 minutes, from Hanger B every 18 minutes, and from hanger C every 24 minutes.  How many... more

Fined the LCM (18,24)

using the prime factorization method 

Prime factorization (6th grade common core math)

A rectangle board game measures 126 cm by 90 cm.  The game board is divided into small squares of equal size. Find the longest possible length of the side of one of the small squares.

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