To find the GCF of numbers.
1. Find the prime factorizations of the numbers.
2. The GCF is the product of the common factors with lower exponent.
a. 36x + 81
Let's start with the prime factorizations.
36 = 2^2 * 3^2
81 = 3^4
The only factor in common is 3. There is a 3^2 and a 3^4. We use 3^2 since it has a lower exponent.
GCF = 3^2 = 9
36x + 81 = 9(4x + 9)
b. 24a + 36
Let's start with the prime factorizations.
24 = 2^3 * 3
36 = 2^2 * 3^2
The two numbers have factor 2 in common. There is a 2^2 and a 2^3, so use 2^2 since it has the lower exponent.
The two numbers have factor 3 in common. There is a 3^2 and a 3. Use 3 since it has the lower exponent.
GCF = 2^2 * 3 = 4 * 3 = 12
24a + 36 = 12(2a + 3)
The factor of the expression (36x + 81) is 9(4x + 9). And the factor of 24a + 36 is 12(2a + 3).
In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
The factor of the first expression will be calculated as below:-
a. 36x + 81
Let's start with the prime factorizations.
36 = 2² x 3²
81 = 3⁴
The only factor in common is 3. There is a 3² and a 3⁴. We use 3² since it has a lower exponent.
GCF = 3² = 9
36x + 81 = 9(4x + 9)
The factor of the second expression will be calculated as below:-
b. 24a + 36
Let's start with the prime factorizations.
24 = 2² x 3
36 = 2² x 3²
The two numbers have factor 2 in common. There is a 2² and a 2³, so use 2² since it has the lower exponent.
The two numbers have factor 3 in common. There is a 3² and a 3. Use 3 since it has a lower exponent.
GCF = 2² x 3 = 4 x 3 = 12
24a + 36 = 12(2a + 3)
Therefore, the factor of the expression (36x + 81) is 9(4x + 9). And the factor of 24a + 36 is 12(2a + 3).
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