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.

 

[Architeuthis Dux]

Yes, you will need to split the numbers in order to find the highest common factor (HCF) for three numbers. The process is similar to finding the HCF for two numbers, but you will need to repeat the process multiple times.

First, find the HCF for two of the numbers using the usual method of finding the factors of each number and identifying the largest common factor. Then, take the HCF you found and compare it to the third number. If the HCF is a factor of the third number, then it is the HCF for all three numbers. If it is not a factor, then you will need to find the HCF for the two numbers again, but this time using the HCF you found in the previous step and the third number.

Repeat this process until you find the HCF that is a factor of all three numbers. This may take a few iterations, but eventually you will find the HCF for all three numbers.

In summary, solving for the HCF for three numbers requires the same process as solving for two numbers, but you will need to repeat the process multiple times using the HCF found in the previous step and the remaining number until you find the HCF that is a factor of all three numbers.