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If you factor by the greatest common factor, you can be assured that there are no common factors left. That is not the case if factoring is by an ordinary common factor.

For example,

3 is a common factor of 30 and 36. 30/36 = 10/12.

But 10 and 12 have a common factor: 2.

6 is the GCF of 30 and 36 and 30/36 = 5/6. 5 and 6 have no common factor (other than 1).

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Q: What is different about factoring with a common factor and factoring by the greatest common factor?

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What makes a greatest common factor "common" is comparing at least two terms and finding something common between them.

In the list of common factors, the greatest is the largest, the least is the smallest (which is always 1)

The greatest common factor of 144 and 175 is 1. Factoring completely, we determine: 144 = 12 * 12 = 3 * 3 * 4 * 4 = 3 * 3 * 2 * 2 * 2 * 2 * 1 175 = 7 * 25 = 7 * 5 * 5 * 1 Since the only factor these have in common is 1, 1 is their greatest common factor.

Yes, the greatest common factor of two different prime numbers is always 1

In order to simplify a rational fraction, you can divide the numerator and denominator by their greatest common factor. However, it is often simpler to divide them both by any common factor (not necessarily the greatest) and then to repeat the process with the resulting fraction. This can be just as fast as finding a large common factor and then carrying out divisions using a large number.

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Factor out the Greatest Common Factor.

factoring whole numbers,factoring out the greatest common factor,factoring trinomials,factoring the difference of two squares,factoring the sum or difference of two cubes,factoring by grouping.

Additive factoring.7e + 7e2= 7e(1 + e)----------------------so,7e=====greatest common factor

What makes a greatest common factor "common" is comparing at least two terms and finding something common between them.

-7xy(x4y2 + 6x2y - 5)

gcf is Greatest Common Factor. It means what is the largest value that can go into what you are factoring.

If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised.

The greatest common factor? Start by factoring both numbers into primes: 25 = 5*5 70 = 2*5*7 The only prime factor in common is a single 5. So the answer is 5.

find a greatest common factor or GCFin factoring a trinomial with a leading coefficient other than 1 the first step is to look for a COMMON factor in each term

You need to learn it, so you can learn Greatest Common Factor, which you need to reduce fractions.

Factoring: 25 = 5x5 and 15 = 5x3. So the factors of 25 and 5 and 5, and the factors of 15 are 3 and 5. The greatest common factor therefore is 5.

One can be a greatest common factor. Though it does not happen often, there are numbers that the only number that they share when factoring is one. An example of this is the numbers two and three. The greatest common factor of two and three is one.

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