Question

How do you find the GCF of 28 and 42?

Answer 1

`GCF(28,42)=color(green)(14)`

Explanation:

Method 1: GCF Algorithm
min `larr` smaller number
max `larr` larger number
rem `larr` remainder of integer division: max `div` min
while rem `!= 0`
`color(white)("XX")`max`larr`min
`color(white)("XX")`min`larr`rem
`color(white)("XX")`rem `larr` remainder of integer division: max `div` min
end_while
GCF`larr`min

`color(white)("XX")`Application with 28 and 42
min `larr` 28
max `larr` 42
rem `larr` 14 (since `42div28=2R14`)
since `14 != 0` do the "while"
`color(white)("XX")`max`larr`28
`color(white)("XX")`min`larr`14
`color(white)("XX")`rem`larr`0 (since `28div14=2R0`)
loop back to re-test loop condition
since `0=0` continue with instructions following the while loop
GCF`larr`14

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Method 2: Collecting Common Prime Factors
Factoring `28`
`color(white)("XX")28=2xx14=2xx2xx7`
Factoring `42`
`color(white)("XX")42=2xx21=2xx3xx7`
Extract common prime factors:
`GCF(cancel(2)xx2xx7,cancel(2)xx3xx7)`
`color(white)("XX")=2xxGCF(2xxcancel(7),3xxcancel(7))`
`color(white)("XX")=2xx7xxGCF(2,3)`
`color(white)("XX")=2xx7xx1`
`color(white)("XX")=14`

Answer 2

14

Explanation:

`" "28=2xx14 = color(red)(2)xx2" "xxcolor(red)(7)`

`ul(" "42=2xx21=color(red)(2)" "xx3xxcolor(red)(7))`
`"common factors"->color(purple)(color(white)(.)2" "7`

So the greatest common factor (GCF) is `2xx7 = 14`