How do you find the GCF of 28 and 42?

Question

Mila Anderson · Accepted Answer

14

#" "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#

Autumn Arnold · Answer

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

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

ด ฟฟ ฟ ฟฟ

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#

Noah Archer · Answer

undefined To find the Greatest Common Factor (GCF) of 28 and 42, you can use either prime factorization or the method of finding common factors.

Prime Factorization:
1. Find the prime factors of each number.
   - Prime factors of 28: 2 * 2 * 7
   - Prime factors of 42: 2 * 3 * 7
2. Identify the common prime factors.
   - The common prime factors are 2 and 7.
3. Multiply these common prime factors together to find the GCF.
   - GCF(28, 42) = 2 * 7 = 14

Method of Finding Common Factors:
1. List all the factors of both numbers.
   - Factors of 28: 1, 2, 4, 7, 14, 28
   - Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
2. Identify the common factors.
   - The common factors are 1, 2, 7, and 14.
3. The greatest common factor among these common factors is 14.

Therefore, the GCF of 28 and 42 is 14.