Question

well heres another chock full of questions:
what is gfc for:
60,45,24,72,32,48,100,30,54,36,3,97,5,4,20,24,36,9,45 and yes im horrible at this.

Answer 1

put it in order first

Answer 2

There isn't a greatest common factor for all of them...e.g. 4 and 45 have no factors in common... Are they supposed to be in pairs?

Answer 3

yes

Answer 4

45 = 3 * 3 * 5
60 = 2 * 2 * 3 * 5
------------------
GCF= 3 * 5 = 15
LCM=2 * 2 * 3 * 3 * 5 = 180

Try the others like that :)

Answer 5

(60,45) (24,72) (32,48) (100,30) (54,36) (3,97,5) (4,20,24) (36,9,45) those are the pairs.

Answer 6

matt101 has given you a good algorithm. Try it on the pair (24,72) and see what you get.

Answer 7

OMG I totally nessed u up last time. I gave u the lcm and noone corrected me

Answer 8

Hey I am sorry so totally ignore the answer I gave u last time

Answer 9

I will go to the previous post and correct it sorry

Answer 10

ok

Answer 11

To find GCF or LCM, first break down your numbers into prime factors, and organize it as I did above. If both numbers share the same factor, put it in the same column, otherwise give the factor its own column. Multiply all the factors that are shared between the two numbers to get the GCF, multiply the numbers from every column to get the LCM.

Try the method above for 24 and 72 and see if you get it.

Answer 12

The prime factorization of 24 is
24 = 2.2.2.3, where . means multiplication.

You find the factorization now for 72 and compare it to 24.

Answer 13

im trying the multiples of 4 to get to 72

Answer 14

It might be easier to break it down as
72 = 8 x 9
Now 8 =2x2x2 and 9 = 3x3
Hence
72 = ... what?

Answer 15

im in 7th just so you know

Answer 16

I gave you the correct answer for that previous one I did give u the gcf

Answer 17

Won't the gcf for all these numbers be 1?

Answer 18

well, you do know that 72 = 8 x 9 yes?

Well if 72 = 8x9 and 8 = 2x2x2 and 9=3x3, it must be that
72 = 8 x 9
= 2x2x2 x 3x3

Answer 19

Is that correct GCF?

Answer 20

@rld613 we're not finding the gcf of all the numbers. But yes, it would be if that were the question.

Answer 21

So what is the question asking?

Answer 22

Now as

24 = 2x2x2x3
72 = 2x2x2x3x3

what is the gcf(24,72)? Look at what matt101 did above.

Answer 23

@rld613: read the thread. It turns out the problem is the find the gcf of a number of pairs and triples of integers. This example, gcf(24,72) is the second problem.

Answer 24

Oh I see

Answer 25

U cld do it the long way like I showed u b4hand

Answer 26

like take every pair and find the factors of each one

Answer 27

i dont understand jamesj. what are you getting at here?

Answer 28

Here is what matt101 did with the first example:
45 = 3 * 3 * 5
60 = 2 * 2 * 3 * 5
------------------
GCF= 3 * 5 = 15

Answer 29

Do you know how to do the factor tree?

Answer 30

Check out what I did above. fourth post down

Answer 31

He found the prime factors in common across both 45 and 60. The product of those factors is the gcf.

Answer 32

i.e. what James just reposted haha

Answer 33

Solike how did ur teacher teach u to find the gcf?

Answer 34

So now, here again is the example for 60 and 45
45 = 3 * 3 * 5
60 = 2 * 2 * 3 * 5
------------------
GCF= 3 * 5 = 15

Apply that to 24 and 72:

24 = 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
-------------------
GCF =

Answer 35

she didnt

Answer 36

ok so basically when I taught it 8th graders i taught it like this

Answer 37

So lets say i took the number 45

Answer 38

@rld613: you're not helping here. We have an algorithm. Unless it is wrong, please stop posting for a minute and let him work the problem.

Answer 39

sorry

Answer 40

But he is in 7th grade that is very young

Answer 41

Y don'y u teach him the long way

Answer 42

Let him try for heaven's sake. For the last time, here again is an example, and here is our problem:


So now, here again is the example for 60 and 45
45 = 3 * 3 * 5
60 = 2 * 2 * 3 * 5
------------------
GCF= 3 * 5 = 15

Apply that to 24 and 72:

24 = 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
-------------------
GCF =

What are the factors in common between 24 and 72?

Answer 43

oh so then isnt it that the gcf is 2 and 3?

Answer 44

there can only be one answer what is the greatest common factor remembeer greatest

Answer 45

oh its 3

Answer 46

Neways sorry for bothering I am gonna go

Answer 47

its ok

Answer 48

yup that is the answer

Answer 49

thanks

Answer 50

James doesn't think so

Answer 51

No it isn't...

Answer 52

24 = 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
-------------------
GCF = 2 x 2 x 2 x 3

The factors in common are 2 and 2 and 2, and 3.

So the gcf(24,72) = 2x2x2x3 = 8x3 = 24

Answer 53

Oh i see what you are doing. I didn't get it

Answer 54

Oh i like this method

Answer 55

Just like the factors in common between 45 and 60 are 3 and 5:
45 = 3 * 3 * 5
60 = 2 * 2 * 3 * 5
------------------
GCF= 3 * 5 = 15

Answer 56

Hence gcf(45,60) = 3x5 = 15.

Answer 57

so then for 60 and 45 it would be 15

Answer 58

Yes.

Try it on your next example:
(32,48)
===========
Remaining problems:
(100,30) (54,36) (3,97,5) (4,20,24) (36,9,45)

Answer 59

First write out the prime factorization
32 = what?
48 = what?

Answer 60

yeah my computer does that alot

Answer 61

32= 4 x 8

Answer 62

Write that as the product of prime numbers. 4 and 8 aren't prime.

Answer 63

4= 2 x 2
8= 4 x 4
right?

Answer 64

no

Answer 65

so then 2 x 2 x 2= 8

Answer 66

yes, hence 32 = ...

Answer 67

i meant to put another 2

Answer 68

What you wrote last was correct. 8 = 2 x 2 x 2, and 4 = 2 x 2.
Hence
32 = 8 x 4
= 2x2x2 x 2x2

Now you factor 48

Answer 69

hint: 48 = 6 x 8

Answer 70

so then i have to do the factors of 2 so that i can get to 6

Answer 71

No. You find whatever the prime factorization of 6 is, whatever it is.

Answer 72

6 = 2 x ...what?

Answer 73

which is 2x3 right?

Answer 74

of course. Hence the prime factorization of 48 is ... what?
48 = ...

Answer 75

48 = 8 x 6
= ...

Answer 76

i think i messed up

Answer 77

8 = 2x2x2 and 6 = 2x3
Hence
48 = 8 x 6
= ...what?

Answer 78

2

Answer 79

what do you mean. 48 does not equal 2. Try that again.

Answer 80

8 = 2x2x2 and 6 = 2x3
Hence
48 = 8 x 6
= ...what?

Answer 81

No you're on the right track. You got the prime factorization of 6, which is 2x3. You found the prime factorization of 8 already, which was 2x2x2. Therefore, the prime factorization of 48, which is 8x6, is what?

Answer 82

no i mean what the common factor is

Answer 83

2

Answer 84

No, that's wrong. Keep with the method here. What is the prime factorization of 48

Answer 85

48 = 8 x 6
= 2x2x2 x 2x3

Now the prime factorization of 32 is
32 = 2x2x2x2x2

Answer 86

i dont know 2 and 3

Answer 87

So comparing factorizations as we have done for the last two problems,

48 = 2 x 2 x 2 x 2 x x 3
32 = 2 x 2 x 2 x 2 x 2
------------------------
gcf =

So what are the prime factors in common across 48 and 32?

Answer 88

Here's the last example again,
24 = 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
-------------------
GCF = 2 x 2 x 2 x 3 = 8 x 3 = 24

Answer 89

So, what's the gcf of 32 and 48?
48 = 2 x 2 x 2 x 2 x x 3
32 = 2 x 2 x 2 x 2 x 2
------------------------
gcf =

What are the prime factors in common across 48 and 32?

Answer 90

\[48=2x2x2x2 and \] im confused

Answer 91

48 = 2 x 2 x 2 x 2 x x 3
32 = 2 x 2 x 2 x 2 x 2
------------------------
gcf = 2 x 2 x 2 x 2 , yes

and 2 x 2 x 2 x 2 = 4 x 4 = 16.

hence the gcf of 48 and 32 is 16.

Answer 92

So look carefully at the three examples.

GCF of 45 and 60:
45 = 3 * 3 * 5
60 = 2 * 2 * 3 * 5
------------------
GCF= 3 * 5 = 15

============

GCF of 24 and 72:
24 = 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
-------------------
GCF = 2 x 2 x 2 x 3 = 8 x 3 = 24

============

GCF of 48 and 32:
48 = 2 x 2 x 2 x 2 x x 3
32 = 2 x 2 x 2 x 2 x 2
------------------------
gcf = 2 x 2 x 2 x 2 = 16

Answer 93

See what we did in each example?

Answer 94

so its 16 not 2 or 3 or
yes

Answer 95

what mean is yes

Answer 96

Here are your remaining problems: GCF of
(100,30)
(54,36)
(3,97,5)
(4,20,24)
(36,9,45)

You do the next one by yourself,really. Step 1, find the prime factorization of 100 and 30. Go.

Answer 97

ok

Answer 98

im doing this the fast way 10x10=100