Question

Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and in exponential form by filling in the boxes for exponents.)

Answer 1

Can someone help me on this I am stuck

Answer 2

Hi! :D

Answer 3

Hi

Answer 4

What two numbers multiply to equal 270?

Answer 5

135*2

Answer 6

Also, welcome to OpenStudy! :D

Answer 7

Thank you

Answer 8

ok

so 270 = 135*2

let's just keep factoring all the numbers until we're left with prime numbers

let's divide 135 by 5. What is 135/5 = ?

Answer 9

27

Answer 10

ok

so 270 = 27*5*2

Let's break down 27.

What is 27/3 = ?

Answer 11

its 9

Answer 12

ok

270 = 9*3*2*5

what is 9/3 = ?

Answer 13

3

Answer 14

9\3 is 3

Answer 15

ok so

270 = 3*3*3*2*5

\(\sf\Large 270 =2* 3^3*5\)

Now let's factor down 360

Answer 16

What 2 numbers multiply to 360? :)

Answer 17

180*2

Answer 18

ok, and

180 /2 = ?

Answer 19

=90

Answer 20

and 90/2 = ?

Answer 21

45

Answer 22

so far we have:

360 = 45 *2*2*2

ok 45/5 = ?

Answer 23

9

Answer 24

=9 sorry about that my computer just froze

Answer 25

and 9/3 = ?

Answer 26

3

Answer 27

it's ok :)

Answer 28

so now we have:

360= 3*3*2*2*2*5


\(\sf\Large 360 = 2^3*3^2 *5\)

Answer 29

\(\sf\Large 270 =2* 3^3*5\)

\(\sf\Large 360 = 2^3*3^2 *5\)

So these are our 2 numbers factored down. :)

So how many "2" are common in 270 and 360?

For example, there is one 2 in 270. And there is three 2's in 360. So they only have in common one 2.

How many 3's are common in between 270 and 360? :)

Answer 30

there is 4 3s

Answer 31

mhmm, not sure how you got 4

we have 3*3*3 in 270

and 3*3 in 360

therefore, they only have two 3's in common

Answer 32

oh my bad

Answer 33

and we have one 5 in common, right? :)

Answer 34

yes

Answer 35

so what is

2 x 3 x 3 x 5 = ?

Answer 36

that is the same thing as 2*3*3*5 = ?

Answer 37

its 90

Answer 38

and that's your GCF of 270 and 360 :)

Answer 39

there was another simple way

you factor 10 out of both 360 and 270

you're left with 36 and 27

then you see that the GCF of 36 and 27 is 9

and then you multiply 10 to everything

so the GCF of 360 and 270 is 90

:P

Answer 40

:) well thx so much for your help

Answer 41

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Answer 42

Anytime! :D