## jakyfraze one year ago 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

1. jim_thompson5910

|dw:1442797970378:dw|

2. 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?

3. jakyfraze

2*630

4. jakyfraze

sorry

5. jakyfraze

630

6. jim_thompson5910

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

7. jim_thompson5910

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

8. jakyfraze

315

9. jim_thompson5910

|dw:1442798355918:dw|

10. 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 = ???

11. jakyfraze

105 :0

12. jakyfraze

wow!!

13. jim_thompson5910

|dw:1442798443090:dw|

14. jim_thompson5910

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

15. jim_thompson5910

what would the complete factor tree look like?

16. jakyfraze

so 2 2 3 3 5 7?

17. 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.

18. jim_thompson5910

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

19. jakyfraze

so why did you stop going down on the left?

20. 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

21. jim_thompson5910

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

22. jim_thompson5910

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

23. jim_thompson5910

1 is NOT a prime number

24. 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?

25. 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

26. jakyfraze

27. jakyfraze

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

28. jim_thompson5910

29. 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

30. jim_thompson5910

and if you want, we can do another example

31. jakyfraze

yes pleas.

32. jakyfraze

I'm going to checkout the website to

33. jim_thompson5910

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

34. jakyfraze

composite number prime factors, what are the difference?

35. 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

36. jim_thompson5910

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

37. jim_thompson5910

|dw:1442799855476:dw|

38. jim_thompson5910

|dw:1442799888145:dw|

39. 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

40. jakyfraze

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

41. 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|

42. 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

43. jakyfraze

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

44. jim_thompson5910

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

45. jim_thompson5910

and you're welcome

46. jakyfraze

i will. can i ask another question?

47. jakyfraze

because i think i got the hang of it :)

48. jakyfraze

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

49. jim_thompson5910

50. 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

51. jim_thompson5910

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

52. 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

53. jakyfraze

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

54. jim_thompson5910

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

55. jakyfraze

lol sorry i meant lol

56. 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

57. jakyfraze

the last one was an accident hahah sorry

58. jim_thompson5910

yep because 625 = 5*5*5*5

59. jim_thompson5910

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

60. jakyfraze

oh my go was just doing something like that

61. jakyfraze

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

62. 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

63. jim_thompson5910

yep 7^5 = 16807

64. jim_thompson5910

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

65. jakyfraze

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

66. jakyfraze

im loving math right now lol

67. jim_thompson5910

I'm glad you're loving math now

68. jakyfraze

yeah! so the last question was right too?

69. jim_thompson5910

the 570,000,000 one? yes it was

70. jakyfraze

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

71. jakyfraze

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