Is it true that $HCF(HCF(a,b),c)=HCF(a,HCF(b,c))$

by Umesh shankar   Last Updated June 30, 2020 03:20 AM - source

If $a,b,c$ are any three positive integers, Is it true that $HCF(HCF(a,b),c)=HCF(a,HCF(b,c))$

My try:

Case $1.$ if atleast one of $a,b,c$ is equal to ONE , then the claim is True.

case $2.$ If every pair is Relatively Prime then the Claim is True

But i will get lot of cases? Any HINT to prove or any counter example to disprove the claim?



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