Question

Which pair of numbers is 4 a common factor of?

Answer 1

@rational

Answer 2

options ?

Answer 3

14 and 20
16 and 24
20 and 42
40 and 50

Answer 4

lets look at the pair in first option : 14 and 20

does 4 divide 14 ?

Answer 5

nope, you would get 3.5.

Answer 6

Yes! there is no need to check second number. eliminate first option and move to next option

Answer 7

ok! :)

Answer 8

so now check if 4 divides into 16?

Answer 9

Yes

Answer 10

yes, it does divide because you get 4.

Answer 11

what about second number

Answer 12

16 and `24`

does 4 divide 24 also ?

Answer 13

yes, you get 6

Answer 14

"4" divides both 16 and 24

that means "4" is a common factor of both 16 and 24

Answer 15

Awesome, thanks!! idk why i could not understand that earlier! :) :D

Answer 16

i see you got it completely now :)
if you're free now, i have a question

Answer 17

ok

Answer 18

we know that "4" is a common factor of "16" and "24"

can you find another common factor ?

Answer 19

hmmmm so another number that divides by 16 and 24?

Answer 20

yes

Answer 21

ok 16 divides by 8 and so does 24, so would that be the greatest?

Answer 22

Very good! I see you really know these stuff well.

16 and 24

8 divides 16
8 divides 24

so 8 is a common factor, but how do you know it is the greatest one ?

Answer 23

not sure.

Answer 24

simple
8 is the greatest common factor because no other numbers greater than 8 divide both 16 and 24

Answer 25

ah i see

Answer 26

"gcd" is the short form form "greatest common divisor" and it is very important number in study of integers:

for example, in our present example we have
gcd(16, 24) = 8

Answer 27

i have another question, what do you do if you have to find a common factor of 3 numbers, for example to find a common factor of 36, 48, and 66. Would i just find a number that divides into all THREE numbers? @rational

Answer 28

so 6 would be a common factor of those numbers, right?

Answer 29

Perfect!!

Answer 30

:D

Answer 31

you may try it like this :

factors of 36 : {1, 2, 3, 4, 6, 9, 12, 18, 36}
factors of 48 : {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}
factors of 66 : {1, 2, 3, 6, 11, 22, 33, 66}

Answer 32

factors of 36 : { `1`, `2`, `3`, 4, `6`, 9, 12, 18, 36}
factors of 48 : { `1`, `2`, `3`, 4, `6`, 8, 12, 16, 24, 48}
factors of 66 : { `1`, `2`, `3`, `6`, 11, 22, 33, 66}

Answer 33

so the common factors are {1, 2, 3, 6}

the greatest common factor is 6

Answer 34

Cool!! I like that way.

Answer 35

Thank you again for all of your help! I like the way you explain things!!