Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

Factoring & Relatively Prime

Factor 49x - 35.

This is what professor Leonard did:

Divide each term by the GCF.

The GCF is 7.

49x ÷ 7 = 7x

-35 ÷ 7 = -5

7(7x - 5)....done!

However, he went on to say that the binomial inside the parentheses is called RELATIVELY PRIME. Leonard stated that the binomial inside the parentheses will always be relatively prime.

What does he mean by those words?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,167

Re: Factoring & Relatively Prime

Relatively prime means the two (or more) numbers have only 1 as a common factor.

For example: 6(= 2 x 3) and 11 are relatively prime, 45( = 3 x 3 x 5) and 77( = 7 x 11) are relatively prime

6 and 15 are not;  as 3 is also a factor of both.

If you factorise out the GCF from an expression then the numbers left must have no common factor because if there was another factor for both then you haven't found the greatest common factor.

So the numbers left are relatively prime.

I'll make up another example.

42x + 70 = 2(21x + 35)  21 and 35 are not relatively prime, but I haven't yet factored out all the common factors.

Let's do that:

42x + 70 = 2(21x + 35) = 14(3x + 5)  Now we have 3 and 5, and these are relatively prime.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

Re: Factoring & Relatively Prime

Relatively prime means the two (or more) numbers have only 1 as a common factor.

For example: 6(= 2 x 3) and 11 are relatively prime, 45( = 3 x 3 x 5) and 77( = 7 x 11) are relatively prime

6 and 15 are not;  as 3 is also a factor of both.

If you factorise out the GCF from an expression then the numbers left must have no common factor because if there was another factor for both then you haven't found the greatest common factor.

So the numbers left are relatively prime.

I'll make up another example.

42x + 70 = 2(21x + 35)  21 and 35 are not relatively prime, but I haven't yet factored out all the common factors.

Let's do that:

42x + 70 = 2(21x + 35) = 14(3x + 5)  Now we have 3 and 5, and these are relatively prime.

Bob

Thanks. Easy to understand now.