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GCF = Greatest Common Factor
This topic wants you to find the largest thing that will divide into each part of a problem.
Let’s start with numbers.
Example 1:
Find the GCF of 10 and 15.
Solution:
A factor is a number that will divide into another number.
10 can be divided by: 1, 2, 5 and 10. These are all the FACTORS of 10.
15 can be divided by: 1, 3, 5 and 15. These are all the FACTORS of 15.
A common factor is a number that BOTH numbers have in common from the list of factors.
The common factors of 10 and 15 are: 1 and 5.
The greatest common factor is the largest number fro the common factor list.
The greatest common factor of 10 and 15 is 5 because it is the largest number.
Example 2: Find the GCF of 12, 16 and 24.
Solution:
The factors of 12 are: 1, 2, 3, 4, 6 and 12.
The factors of 16 are: 1, 2, 4, 8 and 16.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24.
The common factors are 1, 2, and 4.
The greatest common factor is 4 because it is the largest from the list.
Lets try variables (letters).
Problem: Find the GCF of x3y5, x5y4 and x8y.
Solution:
Rename the parts of the problem into the basic meaning:
x3y5 = xxxyyyyy
x7y4 = xxxxxxxyyyy
x8y = xxxxxxxy
xxx are the MOST factors of the letter x and y is the MOST factors of the letter y that these three have parts have in common: so the GCF is x3y.
Problem: a3b6c3, a5b3c7 and ab2c4.
Solution:
a3b6c3 = aaabbbbbbccc
a5b2c7 = aaaaabbccccccc
ab3c4 =abbbcccc
a is the MOST factor of the letter a, bb are the MOST factors of the letter b and ccc are the MOST factors of the letter c that the parts have in common: so the GCF is ab2c3.
Problem: Find the GCF of 6m2n4p3, 9m2n4p3 and 12m4n3p4
Solution:
Find the GCF of the coefficients:
Factors are:
6 = 1, 2 and 3
9 = 1, 3, 9
12 = 1, 2, 3, 4, 6, 12
Common factors are:
1 and 3
Greatest common factor is 3.
Now, work on the letters:
m2n4p3 = mmnnnnppp
m2n4p3 = mmnnnnppp
m4n3p4 = mmmmnnnpppp
mm are the MOST factors of the letter m, nnn are the MOST factors of the letter n and ppp are the MOST factors of the letter that the parts have in common: so the GCF is m2n3p3.
Then write your FINAL answer for the problem:
The GCF is 3 m2n3p3.
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Mathematics