1. ## Prime Factorization Help

Hi All.

Im not actually at high school, im at college but i felt this is at high school level. I'm doing a Web Development degree at uni next work and need to brush up on my algebra.

First of all i understand how to do Prime Factorization with integers, eg: Find PF of 459:

Code:
459/3
153/3
51/3
17

459 = 3 x 3 x 3 x 17 (dont know how to right exponents on this forum)
What about when working with floating point (decimal)? Does PF Only work with integers?

Also last question, is it appropriate to use a calculator when trying to find the PF on a number? Without a calculator the process takes a while, when doing exams would i be expected to use a calculator when trying to find the PF of a number with more then 5 digits?

Thanks

2. i just tryed a random number, such as 84961 and nothing goes into it, apart from 1. Is that correct? so 84961 cannot be a prime number thus cannot be factorized yes?

3. Originally Posted by JJ07
Hi All.

Im not actually at high school, im at college but i felt this is at high school level. I'm doing a Web Development degree at uni next work and need to brush up on my algebra.

First of all i understand how to do Prime Factorization with integers, eg: Find PF of 459:

Code:
459/3
153/3
51/3
17

459 = 3 x 3 x 3 x 17 (dont know how to right exponents on this forum)
What about when working with floating point (decimal)? Does PF Only work with integers?

What do you think the purpose of prime factorisation of a float might be?
Since primes are integers, the product of primes is also an integer, so a
product of primes can never equal a float that is not an exact integer.

RonL

4. Originally Posted by JJ07
i just tryed a random number, such as 84961 and nothing goes into it, apart from 1. Is that correct? so 84961 cannot be a prime number thus cannot be factorized yes?
84961 is prime so it is in a sense its own prime factorisation.

RonL

5. on this topic not really answering your question. My friend did his thesis on Prime factorisation.

http://www.cs.bath.ac.uk/~amb/CM3007...ion-2006-7.pdf

he has some good basic stuff and lots of algorithms

6. Originally Posted by chogo
on this topic not really answering your question. My friend did his thesis on Prime factorisation.

www.cs.bath.ac.uk/~amb/CM30076/projects.bho/2006-7/Kanabar-KA-dissertation-2006-7.pdf

he has some good basic stuff and lots of algorithms

It is full of mistakes/misprints, or at least the first three pages of
chapter 2 are, and I doubt many people engaged on original research
would agree with section 1.3 either.

RonL

7. yeah i certainly wont!

8. Hello, JJ07!

Prime Factorization is always with integers.

There is no formula for checking for primes.

There are some "eyeball" tricks for divisibility.
. . You probably know most of these.

. . Divisible by 2: the number ends in an even digit (0,2, 4, 6, 8).
. . Divisible by 3: the sum of its digits is divisible by 3.
. . Divisible by 4: the rightmost two-digit number is divisible by 4.
. . Divisible by 5: the number ends in 0 or 5.
. . Divisible by 9: the sum of its digits is divisible by 9.

If you can't "see" a factor by inspection,
. . the procedure is to divide by consecutive primes
. . and see if any division "comes out even".

You might memorize the first few primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, ...

And yes, I believe you're allowed to use a calculator for this.

Example: $31,668$

It is even; divide by 2: . $31,668 \div 2 \:=\:15,834$ . . . 2 is a factor.

The quotient is still even; divide by 2: . $15,834 \div 2 \:=\:7917$ . . . 2 is a factor.

The quotient is not even; it is not divisible by 2.
Try dividing by 3: . $7917 \div 3 \:=\:2639$ . . . 3 is a factor.

. . Try dividing by 3 again: . $2639 \div 3 \:=\:879.666...$ no

We try dividing by 5, but we can see that it is not divisible 5, right?

Try dividing by 7: . $2639 \div 7 \:=\:377$ . . . 7 is a factor.

. . Try 7 again: . $377 \div 7 \:=\:53.8571...$ no

Try dividing by 11:. . $377 \div 11 \:=\:34.2727...$ no

Try dividing by 13: . $377 \div 13 \:=\:29$ . . . 13 is a factor.

. . Since 29 is a prime, we are done.

"Collect" the factors: . $31,668 \;=\;2^2 \times 3 \times 7 \times 13 \times 29$

9. Thanks for that last reply, really helped me out, i have been practicing all day and have gotten used to it.

Im kind of confused on 'Reducing Factors'. Infact im very confused. The thing is right, its not that im incompetent, far from it, but at school you had a teacher who taught you the right way on doing things, at home all i have is the internet, and everywere is teaching different methods and ways around things and im boggled, and infact a bit annoyed because im finding it hard to remember.

Basically without looking at any manuals or websites, this is how i think i should 'Reduce Factors':

56 over 108, now i must find all the prime factors that both the nominator and denominator share, by doing 'Prime Factorization', starting at the lowest prime (2), which works out to:

56/2 = 28
28/2 = 14
14/2 = 7

108/2 = 54
54/2 = 27
27/3 = 9
9/3 = 3

And now im stuck, i tried to think of what i do next but just cant.

Im starting to feel like a loser, 22 and cant even do basic algebra. One source is saying you use the Greatest Common Factor, the other source is a book i have which is supposed to be teaching people from the ground up, but it seems to confuse more then anything, which tells me:
Next collect the primes common to both
the numerator and denominator (if any) at beginning of each fraction. Split
each fraction into two fractions, the first with the common primes. Now the
fraction is in the form of ‘‘1’’ times another fraction.
Can anyone recommend a good book for me please, i have Algebra Dymistified which is not as easy at it claims, not for me anyway.

10. Originally Posted by JJ07
Im kind of confused on 'Reducing Factors'. Infact im very confused. The thing is right, its not that im incompetent, far from it, but at school you had a teacher who taught you the right way on doing things, at home all i have is the internet, and everywere is teaching different methods and ways around things and im boggled, and infact a bit annoyed because im finding it hard to remember.

Basically without looking at any manuals or websites, this is how i think i should 'Reduce Factors':

56 over 108, now i must find all the prime factors that both the nominator and denominator share, by doing 'Prime Factorization', starting at the lowest prime (2), which works out to:

56/2 = 28
28/2 = 14
14/2 = 7

108/2 = 54
54/2 = 27
27/3 = 9
9/3 = 3

And now im stuck, i tried to think of what i do next but just cant.
So you now have:
$\frac{108}{56} = \frac{2^2 \cdot 3^3}{2^3 \cdot 7}$

Group together the factors that are common to both the numerator and denominator:
$= \frac{(2 \cdot 2) \cdot (3^3)}{(2 \cdot 2) \cdot (2 \cdot 7)}$

Cancel the two common factors of 2 in the numerator and denominator:
$= \frac{3^3}{2 \cdot 7}$

$= \frac{27}{14}$

-Dan

11. Hello, JJ07!

The way you reduce fractions is correct,
. . but it can be done faster by "cancelling".

Example: . $\frac{56}{108}$

We see that both numbers are even; they are divisible by 2.

. . Cancel 2's: . $\frac{56 \div 2}{108 \div 2} \:=\:\frac{28}{54}$

Both numbers are still even; they are divisible by 2.

. . Cancel 2's: . $\frac{28 \div 2}{54 \div 2} \:=\:\frac{14}{27}$

14 is divisible by 2 and 7 . . . 27 is divisible by 3 and 9.
. . No more cancelling is possible.

Therefore, the fraction is in lowest terms: . $\frac{14}{27}$

12. ## Re: Prime Factorization Help

Originally Posted by JJ07
i just tryed a random number, such as 84961 and nothing goes into it, apart from 1. Is that correct? so 84961 cannot be a prime number thus cannot be factorized yes?
Your understanding is not quite correct. You are right in saying that 84961 cannot be factorized, but *because* 84961 has no prime factors (it is only divisible by 1 and itself), it is a Prime Number.

You can check whether or not an integer is a prime number via online web sites such as this one: Prime Factors Function