What is the greatest common factor of 42, 63, and 105?

Question

Noah Archer · Accepted Answer

The greatest common factor of #42, 63, and 105# is #21#

The smallest prime numbers (prime numbers 2, 3, 5, 7, 11, 13, 17, 19) should be divided into each of the other given numbers to find the greatest common factor (GCF), which is the largest number that will divide into all of the given numbers.

Looking at #42, 63, 105,# we can see that the first is divisible by #2#, the second by #3# and the third by #5#:

#42/2=21# and #63/3=21# and #105/5=21#

The GCF is the same number that is obtained from each division.

Jeremiah Andrews · Answer

Greatest Common Factor is #21# Factors of #42# are #{1,2,3,6,7,14,21,42}# Factors of #63# are #{1,3,7,9,21,63}# Factors of #105# are #{1,3,5,7,15,21,35,105}# Common factors are just #{1,3,7,21}# and Greatest Common Factor is #21#.

Aurora Arias · Answer

#HCF =21#

Finding the HCF and LCM of any number of values can be done quickly by writing each number as the product of its prime factors.

#" " 42 = 2xxcolor(blue)(3xx" "7)# #" "63 = " "color(blue)(3)xx3xxcolor(blue)(7)# #" "ul(105= " "color(blue)(3 xx" "7) xx 5)# #HCF =color(white)(xxx)color(blue)(3xx" "7)" "= 21#

#42,63 and 105# all have the factors #3 and 7# in common.

Therefore the #HCF =21#

Gianna Caruso · Answer

undefined The greatest common factor (GCF) of 42, 63, and 105 is 21.

Aurora Arias · Answer

undefined The greatest common factor (GCF) of 42, 63, and 105 is 21.