Question

Find the greatest common factor of thefollowing monomials:6m3n2 m5 n52mn3

Answer 1

So we have the following set of terms:

`6m^3n,2m^5n^5,2mn^3`

The greatest common factor (from now on, GCF) is a term that meets the following:

- All the three terms are multiples of it.

- It's the greatest number with the greatest power of each variable that meets the condition above.

One way to find it is looking for the GCFs of the integers, the powers of m and the powers of n separately. For example, the integers present in the set of three terms are 6, 2 and 2. If we factor each of them we get:

`2\cdot3,2,2`

The only number that appears in the 3 factored numbers is 2 so the GCF of the integers is 2.

Then we have to find the GCF among the powers of m. When you look for the GCF of a set of powers of the same variable the result is the power with the smallest exponent so if the powers we have are:

`m^3,m^5,m`

Then the GCF is m because its exponent is 1 whereas the other two exponents 3 and 5 are greater.

If we do the same for the powers of n we have:

`n,n^5,n^3`

Again, the GCF is the power of n with the lowest exponent, in this case n.

Now that we have found the GCFs of the integers, the powers of m and the powers of n we can find the GCF of all the terms. This is given by the product of those 3. Then the answer is:

`2mn`