Solving for Highest Common Factor (HCF) with 3 Numbers

[garyljc]

when i come across hcf , i can solve for hcf for 2 numbers, but if the hcf requires 3 ?
do i need to split them ?

 

[HallsofIvy]

Do you mean the "hcf" or "highest common factor" (also called the "greatest common divisor") of three or more numbers? It doesn't really matter how many numbers you have you do the same thing: Find all prime factors of each number and see how many prime factors they all have in common. The "highest common factor" is the product of those prime factors. If they have no prime factors in common, the "highest common factor" is 1.

For example, 12, 6, and 8 factor as 2²*3, 2*3, and 2³. The last number has no factor of 3. While each has a factor of 2, 6 has only one 2: the highest common factor is 2.

If it were 14= 2*7, 8= 2³, and 21= 3*7, since 8 has only 2 as prime factor and 21 does not have a factor of 2, they have no prime factors in common: the highest common factor is 1.