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# Greatest Common Divisor

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##### Description:

At the end of this lesson,

1. Students will be able to correctly find Greatest Common Divisor using common factor of two or more numbers,

2. Students will be able to explain verbally their thought processes in doing so.

3. Students will be able to solve problems using Greatest Common Divisor.

The greatest common factor is especially useful for the reduction of fractions to their lowest terms.

It is done by dividing both the numerator and denominator with their greatest common factor, thus finding

an equivalent fraction in which the numerator and denominator are as small as they can possibly be.

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Tutorial

## Greatest Common Factor

The Greatest Common Factor of two or more numbers (also called the greatest common factor or the

highest common factor or the greatest common divisor) is the largest number that gives an integer as a result when

both numbers are divided by it.

The easiest way to calculate the GCF of two numbers is to list all the factors of those numbers and

choose the ones they have in common. The largest of those factors is the greatest common divisor.

For example,  look at the numbers 27 and 45 and calculate their GCF

The number 27 can be divided by numbers 1, 3 and 9.

The number 47 is divisible by numbers 1, 3, 5, 9 and 15.

The divisors they have in common are 1, 3 and 9.

The largest of them is 9 and it is their greatest common divisor.

It is also possible to calculate the GCF by using prime factorizations and determining

how many factors the two numbers have in common.

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