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Greatest Common Factor

1,190 views · Published 28 June 2012 · 3:15 · Indexed 11 October 2026

Channel: MooMooMath and Science · 2012 · Education

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Learn how to find the greatest common factor.  the greatest common factor. Here are our first examples in fast form. 

Let's look at 30 the first thing I'm going to factor is 5 times 6, the 5 is prime so I don't bring it down, next 6 equals it 3 three times 2 so I write a 5 times 2 times 3. Now let's do a factor three of 42, that 6 times 7, 6 is composite and 7 is prime so I'm done with that one so now I can factor the 6 down to 2 times 3 so the prime factorization is 2 times 3 times 7, so I circle my common factors and multiply so my greatest common factor is 6. Now let's slow it down and look at the rules of greatest common factor.

1. Complete prime factorization for each number. This includes drawing a factor tree for each number and factor down to prime numbers.
2. Pair the common factors. ( It may help to circle all the factors that are common )
3. Take the common factors (the ones that you circled) and multiple them back together and this gives you your Greatest common factor.

 Why is it important to find the GCF?
Finding the greatest common factor (GCF) is important for several reasons:
Simplifying Fractions: If two numbers have a common factor, you can simplify the fraction by dividing both the numerator and denominator by the GCF. This makes the fraction easier to work with and compare to other fractions.
Solving Equations: When solving equations, it is often helpful to factor the terms in the equation. If the terms have a common factor, you can factor it out and simplify the equation. This can make it easier to solve for the unknown variable.
Reducing Radicals: When simplifying radicals, it is important to find the largest perfect square factor of the radicand. This allows you to rewrite the radical in a simpler form.
Simplifying Polynomials: When simplifying polynomials, it is often helpful to factor out the greatest common factor of all the terms. This can make the polynomial easier to work with and expand.

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