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to find the prime factorization, we divide by small numbers. let's pick a small number like 2 what is 1260/2 equal to?
yes, so because 1260 = 2*630, we draw two branches like this |dw:1442798244739:dw|
then we do the same with 630 630/2 equals ???
then we do 315/2 = 157.5 which is not a whole number so we try another small number like 3 315/3 = ???
we keep going down the line until everything is broken up into prime numbers
what would the complete factor tree look like?
so 2 2 3 3 5 7?
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.
circle the primes then multiply them all out |dw:1442798698121:dw|
so why did you stop going down on the left?
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
|dw:1442798869349:dw| and so on...
so that's why 1 is left out of the factor tree
1 is NOT a prime number
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?
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
hmm. were can i go to learn about this a little more
i really want to learn this more because i new to this
this page has good tutorial and example http://study.com/academy/lesson/what-is-a-factor-tree-definition-example.html
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
and if you want, we can do another example
I'm going to checkout the website to
ok pick any number you like that's relatively small, but big enough to factor
composite number prime factors, what are the difference?
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
so think of "composite" as "composed of other smaller things" like composite wood
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
oh my god THANK YOU. so how is the circle numbers prime?
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|
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
ohhh thank you, how did you know all of this? thank you @jim_thompson5910
Lots and lots of practice. You'll get better at it by practicing it as much as possible.
and you're welcome
i will. can i ask another question?
because i think i got the hang of it :)
@jim_thompson5910 i will. can i ask another question? i think i got the hang of it :)
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
2 × 2 × 5 × 5 × 7 is correct. Nice job
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
yes!!! I'm going to continue practicing, to be like you :)
25 is NOT prime. Why? because it can be factored further 25 = 5*5
lol sorry i meant lol
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
the last one was an accident hahah sorry
yep because 625 = 5*5*5*5
there are 4 copies of 5 being multiplied, we can use this shortcut \[\Large 625 = 5*5*5*5 = 5^4\]
oh my go was just doing something like that
What is the value of 7 to the fifth power? A. 2,401 B. (16,807) My answer C. 35 D. 78,125
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
yep 7^5 = 16807
and yes, 5.7 * 10^8 = 570,000,000 570,000,000 = 570 million
oh my god I'm so happy right now :D. Thank you for everything you where a really big help for me,
im loving math right now lol
I'm glad you're loving math now
yeah! so the last question was right too?
the 570,000,000 one? yes it was
oh man thank you :'). I'm about to submit my exam :D
@jim_thompson5910 i got a 100!! thank you thank thank you. and god bless you :)