What is the hcf of #25# and #5#?

3 Answers
Jan 23, 2018

#5#

Explanation:

#"one way is to use a "color(blue)"division method"#

#• " divide the larger number by the smaller"#

#• " if the remainder is zero then the smaller number is HCF"#

#• " if remainder is not zero repeat the process"#

#rArr35/25=1color(blue)" remainder 10"#

#["repeat with 25 and 10"]#

#rArr25/10=2color(blue)" remainder 5"#

#[" repeat with 10 and 5"]#

#rArr10/5=2color(blue)" remainder 0"larrcolor(red)"zero remainder"#

#rArrHCF" of 25 and 35 "=5#

Jan 24, 2018

#hcf(25,35)=5#

Explanation:

another approach: list all the factors of each number and choose the commons one, and hence the hcf

factors#" "25:{color(red)(1,5),25}#

factors #" "35:{color(red)(1,5),7,35}#

common factors#" "{1.5}#

#:.hcf(25,35)=5#

Jan 25, 2018

The hcf(25,35) is #5#.

Explanation:

The hcf (highest common factor) is the same as the gcf (greatest common factor). There are two ways to find the hcf. You can list the factors of each number and identify the greatest factor in common. You can also you prime factorization.

Listing factors

#25:##1,color(red)5,25#

#35:##1,color(red)5,7,35##

#"hcf(25,35)"=color(red)5"#

Listing prime factors

#25:##color(red)5xx5#

#35:##color(red)5xx7#

Since there is one #5# in the factorization of #35#, we only count the #5# one time in determining the hcf.

#"hcf(25,35)"=color(red)5"#