Finding The Greatest
Common Factor
Greatest Common Factor
The greatest common factor is the largest
common factor of two numbers. Factors
are all of the numbers that divide into a
given number equally.
The greatest common factor can be found by
comparing all the factors of two numbers
or by finding the prime factorization of
two numbers
Finding Factors
Finding the factors of a number can be
done by sequentially dividing numbers
into the product. When the factors
begin to repeat you have found all
factors.
Finding Factors
Find the factors of 18
1 goes into 18, 18 times.
2 goes into 18, 9 times.
3 goes into 18, 6times.
4 does not divide 18 evenly.
5 does not divide 18 evenly.
We are now back to 6. We have found all factors of
18.
1, 2, 3, 6 and 18
Finding The GCF Using
Factors
Determine the greatest common factor
of two numbers by finding all the
factors for the two numbers then
comparing them. The largest common
factor of the two numbers is their
greatest common factor.
Using Factors
Find the GCF of 36 and 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36
Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
The greatest common factor is of 36 and 24
is 12
Using Factors Again
Find the GCF of 15 and 100
Factors of 15: 1, 3, 5 and 15
Factors of 100: 1, 2, 4, 5, 10, 20, 25,
50 and 100
The greatest common factor of 15 and 100 is 5
Finding the Prime
Factorization
A prime factorization is when a
product is broken down until only
prime numbers remain. Prime
numbers are numbers who’s only
factors and 1 and them self. A
factor tree is useful in finding a
prime factorization.
Prime Factorization
Break 18 down to only prime numbers.
18
/\
2 9
/\
3 3
18 = 2 × 2 × 3
Finding the GCF Using
Prime Factorization
To determine the greatest common
factor find the prime factorization
for each number. Find all of the
common prime factors of the two
numbers and multiply them together.
Your sum is the GCF.
Using Prime
Factorization
Find the GCF of 36 and 24
36 24
/\ /\
2 18 2 12
/\ /\
2 9 2 6
/\ /\
3 3 2 3
36= 2×2×3×3 24= 2×2×2×3
The GCF of 36 and 24 is 2×2×3=12
Using Prime
Factorization Again
Find the GCF of 21 and 42
21 42
/\ /\
3 7 2 21
/\
3 7
21 = 3×7 42 = 2×3×7
The GCF of 21 and 42 is 3×7 = 21
Greatest Common Factor
Now you know how to find the
greatest common factor you if you
have any other questions check out
these sites about finding the GCF
Greatest Common Factor
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