Transcript GREATEST COMMON FACTOR

GREATEST COMMON FACTOR
Eduardo Lira
GREATEST COMMON FACTOR
In mathematics, the greatest common divisor (gcd),
also known as the greatest common denominator,
greatest common factor (gcf), or highest common
factor (hcf), of two or more non-zero integers, is the
largest positive integer that divides the numbers
without a remainder.
OVERVIEW
The greatest common divisor is useful for reducing
fractions to be in lowest terms. For example, gcd
42/56 = 14, therefore,
42 divided by 14 = 3 and 56 divided by 14 = 4,
so 42/56 = 3/4
USING PRIME FACTORIZATIONS
Greatest common divisors can be calculated by
determining the prime factorizations of the two
numbers and comparing factors.
EXAMPLE
To calculate the gcd of 18/84, we find
the prime factorizations: 18 = 1, 2, 3,
6, 9, 18 and 84 = 1, 2, 3, 4, 6, 7, 12, 14,
16, 21, 28, 42, 84, and notice that the
"overlap" of the gcf is 6, so the gcd
of 18/84 = 6.
EXAMPLE
Factors are the numbers you multiply together to get
another number:
.
Sometimes we want to find all the factors of a number:
the factors of 12 are 1,2,3,4,6 and 12 ...
because 2 × 6 = 12, or 4 × 3 = 12, or 1 × 12 = 12.
The greatest common factor, or GCF, is the
greatest factor that divides two numbers. To
find the GCF of two numbers:
List the prime factors of each number.
Multiply those factors both numbers have in
common. If there are no common prime factors,
the GCF is 1.
QUESTION
What is the greatest common factor of
15 and 5?
The answer is 5
because 15 = 3x5 and 5 = 1 x 5.
GREATEST COMMON FACTOR
The Greatest Common Factor (GCF) is the largest number that is a
common factor of two or more numbers.
How to find the greatest common factor:
Determine if there is a common factor of the numbers. A common
factor is a number that will divide into both numbers evenly. Two is a
common factor of 4 and 14.
Divide all of the numbers by this common factor.
Repeat this process with the resulting numbers until there are no
more common factors.
Multiply all of the common factors together to find the Greatest
Common Factor.