someone please help me :"(
What is the prime factorization of 1,260?
A. 2 × 3 × 5 × 6 × 7
B. 4 × 5 × 7 × 9
C. 2 × 2 × 3 × 3 × 5 × 7
D. 2 × 3 × 5 × 7

- jakyfraze

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- jim_thompson5910

|dw:1442797970378:dw|

- jim_thompson5910

to find the prime factorization, we divide by small numbers. let's pick a small number like 2
what is 1260/2 equal to?

- jakyfraze

2*630

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## More answers

- jakyfraze

sorry

- jakyfraze

630

- jim_thompson5910

yes, so because 1260 = 2*630, we draw two branches like this
|dw:1442798244739:dw|

- jim_thompson5910

then we do the same with 630
630/2 equals ???

- jakyfraze

315

- jim_thompson5910

|dw:1442798355918:dw|

- jim_thompson5910

then we do 315/2 = 157.5 which is not a whole number
so we try another small number like 3
315/3 = ???

- jakyfraze

105 :0

- jakyfraze

wow!!

- jim_thompson5910

|dw:1442798443090:dw|

- jim_thompson5910

we keep going down the line until everything is broken up into prime numbers

- jim_thompson5910

what would the complete factor tree look like?

- jakyfraze

so 2 2 3 3 5 7?

- jim_thompson5910

yeah if we keep going, we'd have
105/3 = 35
35/5 = 7
|dw:1442798627134:dw|
as you can see, the tree gets big pretty fast. Luckily we're done at this point because we have nothing but primes left.

- jim_thompson5910

circle the primes then multiply them all out
|dw:1442798698121:dw|

- jakyfraze

so why did you stop going down on the left?

- jim_thompson5910

because we can't break up 2 or 3 into smaller pieces. The primes are the "atomic" elements so to speak.
I guess we could say 2 breaks down into 2*1, but then we'd be stuck doing that forever. The tree would never end

- jim_thompson5910

|dw:1442798869349:dw|
and so on...

- jim_thompson5910

so that's why 1 is left out of the factor tree

- jim_thompson5910

1 is NOT a prime number

- jakyfraze

ohh so your saying that if the left side had a 3 it would go down anther step instead of 1 step like the 2?

- jim_thompson5910

yeah 3 is also prime so we can't break that down any further. If we include 1 as a factor, then we'd be at it forever

- jakyfraze

hmm. were can i go to learn about this a little more

- jakyfraze

i really want to learn this more because i new to this

- jim_thompson5910

this page has good tutorial and example
http://study.com/academy/lesson/what-is-a-factor-tree-definition-example.html

- jim_thompson5910

That's good you want to learn more about it. Let me know if the page helps or not. If not, then I'll find another page

- jim_thompson5910

and if you want, we can do another example

- jakyfraze

yes pleas.

- jakyfraze

I'm going to checkout the website to

- jim_thompson5910

ok pick any number you like that's relatively small, but big enough to factor

- jakyfraze

composite number prime factors, what are the difference?

- jim_thompson5910

a composite number is a number that can be factored into smaller primes
eg: 10 is composite because 10 = 2*5
2 and 5 are prime numbers. They cannot be factored into anything but 1 and themself
2 = 2*1 and that's it
5 = 5*1 and that's it

- jim_thompson5910

so think of "composite" as "composed of other smaller things"
like composite wood

- jim_thompson5910

|dw:1442799855476:dw|

- jim_thompson5910

|dw:1442799888145:dw|

- jim_thompson5910

here is a cool interactive lesson to play with
http://www.mathplayground.com/factortrees.html
click on the "find the prime factorization of 1 number", then you'll be led to an interactive prompt where you type in the numbers to factor various numbers

- jakyfraze

oh my god THANK YOU. so how is the circle numbers prime?

- jim_thompson5910

well we cannot factor a number like 2 any further. When I say "factor" I mean "find two whole numbers that multiply to this number"
we can say 2 = 2*1, but 1 isn't prime, so we can't break down 2 further. Any primes that you find on the factor tree are circled so you remember to go back and use them in the final multiplication (like you see below)
|dw:1442800545730:dw|

- jim_thompson5910

3, 5 and 7 are prime for the same reasons as 2 is
for 3, the only two numbers that multiply to 3 are 3 and 1. There are no other factors. So 3 is prime. Same for 5 and 7

- jakyfraze

ohhh thank you, how did you know all of this? thank you @jim_thompson5910

- jim_thompson5910

Lots and lots of practice. You'll get better at it by practicing it as much as possible.

- jim_thompson5910

and you're welcome

- jakyfraze

i will. can i ask another question?

- jakyfraze

because i think i got the hang of it :)

- jakyfraze

@jim_thompson5910 i will. can i ask another question? i think i got the hang of it :)

- jim_thompson5910

go ahead

- jakyfraze

thank you :).
What are the prime factors of 700?
A. 350 × 2
B. 2 × 2 × 2 × 5 × 5 × 7
C. (2 × 2 × 5 × 5 × 7) My answer
D. 2 × 2 × 25 × 7

- jim_thompson5910

2 × 2 × 5 × 5 × 7 is correct. Nice job

- jakyfraze

What are the prime factors of 625?
A. 1, 5, 5, 5, 5
B. (5, 5, 25) My answer
C. 5, 5, 5, 5
D. 25, 25

- jakyfraze

yes!!! I'm going to continue practicing, to be like you :)

- jim_thompson5910

25 is NOT prime. Why? because it can be factored further
25 = 5*5

- jakyfraze

lol sorry i meant lol

- jakyfraze

What are the prime factors of 625?
A. 1, 5, 5, 5, 5
B. 5, 5, 25
C. (5, 5, 5, 5) My answer
D. 25, 25

- jakyfraze

the last one was an accident hahah sorry

- jim_thompson5910

yep because 625 = 5*5*5*5

- jim_thompson5910

there are 4 copies of 5 being multiplied, we can use this shortcut
\[\Large 625 = 5*5*5*5 = 5^4\]

- jakyfraze

oh my go was just doing something like that

- jakyfraze

What is the value of 7 to the fifth power?
A. 2,401
B. (16,807) My answer
C. 35
D. 78,125

- jakyfraze

What is the value of 5.7 × 108?
A. 57,000,000
B. (570,000,000) My answer
C. 5,700,000,000
D. 5.70000000

- jim_thompson5910

yep 7^5 = 16807

- jim_thompson5910

and yes, 5.7 * 10^8 = 570,000,000
570,000,000 = 570 million

- jakyfraze

oh my god I'm so happy right now :D. Thank you for everything you where a really big help for me,

- jakyfraze

im loving math right now lol

- jim_thompson5910

I'm glad you're loving math now

- jakyfraze

yeah! so the last question was right too?

- jim_thompson5910

the 570,000,000 one? yes it was

- jakyfraze

oh man thank you :'). I'm about to submit my exam :D

- jakyfraze

@jim_thompson5910 i got a 100!! thank you thank thank you. and god bless you :)

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