Factor 18m − 24n using the GCF. (1 point)
To factor 18m − 24n using the greatest common factor (GCF), we need to find the largest number that can divide both 18m and 24n. In this case, the GCF is 6, because 6 is the largest number that can divide evenly into 18 and 24.
Therefore, we can rewrite 18m and 24n as:
18m = 6 * 3 * m
24n = 6 * 4 * n
Now we can factor out the GCF from both terms:
18m − 24n = 6 * 3 * m − 6 * 4 * n
Now we can factor out the common factor of 6:
= 6 * (3m − 4n)
Therefore, 18m − 24n can be factored as 6(3m − 4n).
To factor out the greatest common factor (GCF) from the given expression 18m - 24n, we need to find the largest number or term that can evenly divide into both 18m and 24n.
Step 1: Find the GCF of the coefficients 18 and 24.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The common factors of 18 and 24 are 1, 2, 3, and 6.
So, the GCF of 18 and 24 is 6.
Step 2: Find the GCF of the variables m and n.
Since there are no common factors between m and n, the GCF of m and n is 1.
Step 3: Write the GCF as a factor outside the parentheses.
The GCF of the entire expression 18m - 24n is 6.
Step 4: Divide the expression by the GCF.
(18m - 24n) ÷ 6 = 3m - 4n
Therefore, the completely factored form of 18m - 24n using the GCF is 6(3m - 4n).
To factor 18m - 24n using the greatest common factor (GCF), we need to find the highest common factor of 18m and 24n.
Step 1: Find the GCF of 18m and 24n.
To find the GCF, we need to break down 18m and 24n into their prime factorization.
The prime factorization of 18m can be found by dividing 18 by its prime factors and separating out the "m" term:
18m = 2 × 3^2 × m
The prime factorization of 24n can be found by dividing 24 by its prime factors and then separating out the "n" term:
24n = 2^3 × 3 × n
Step 2: Identify the common factors.
To find the GCF, we look for the common prime factors in both 18m and 24n:
Common factors: 2, 3
Step 3: Determine the highest common factor.
The highest common factor is the product of the common prime factors raised to the lowest exponent they appear in either number:
GCF = 2 × 3 = 6
Step 4: Factor out the GCF.
To factor 18m - 24n using the GCF, we divide each term by the GCF and bring the GCF outside the parentheses:
18m - 24n = 6(3m - 4n)
Therefore, the final factored form of 18m - 24n using the GCF is 6(3m - 4n).