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# Greatest common factor homework help

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

In this video, learn how to find the greatest common factor of two numbers. Then, see how this can be used to solve problems with large numbers. In the accompanying classroom activity, students learn to find prime factors using factor trees. They then learn how prime factors, a Venn diagram, and simple multiplication can help them find the greatest common factor of two numbers. The lesson challenges students to find the greatest common factor of increasingly large numbers. It also pushes them to think about how prime factors are the building blocks of composite numbers. This resource is part of the  Math at the Core: Middle School Collection .

Let's start by looking at the factors of 6. The factors of 6 are going to be 2 and 3, because 2 x 3 = 6. It's also true that 1 and 6 are factors, then, because 1 x 6 is also equal to 6. That gives us our full list for the factors of 6 as 1, 2, 3, and 6.

To find the GCF by factoring, list out all of the factors of each number or find them with a Factors Calculator . The whole number factors are numbers that divide evenly into the number with zero remainder. Given the list of common factors for each number, the GCF is the largest number common to each list.

Therefore, 7 * 7 * 5 * 2 = 490. Those four numbers circled in red are all prime and cannot be factored anymore, so you must be done. That is the prime factorization of 490. Now you can do the same with your other number, 819.

This notion can be extended to polynomials (see Polynomial greatest common divisor ) and other commutative rings (see below ).

Find the GCF of each set of three numbers. The easy level has numbers up to 25 and the medium level has numbers up to 100.

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Greatest common factor explained (video) | Khan Academy

Greatest common divisor - Wikipedia

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greatest common factor homework help
greatest common factor homework help