Reviewed by Marvi M. Andres
What is the greatest common factor of 4k, 18k4, and 12?
Answer: The greatest common factor of 4k, 18k4, and 12 is 2
The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest integer that evenly divides two or more given numbers or algebraic expressions. For algebraic terms, the GCF is determined by finding the largest numerical factor and the highest power of any common variable present in all terms. In this problem, we are asked to find the GCF of the terms 4k, 18k⁴, and 12.
Methods
Math Tutor Explanation Using Prime Factorization Method
This method involves breaking down the coefficients into their prime factors and analyzing variables in the terms.
Step 1: Write the prime factorization of each coefficient: 4 = 2 × 2, 18 = 2 × 3 × 3, 12 = 2 × 2 × 3
Step 2: Identify the lowest power of each common prime across all coefficients; 2 is common to all coefficients. The lowest power of 2 present is one occurrence
Math Tutor Explanation Using Listing Factors Method
By listing the factors of each term and identifying the largest factor common to all, we can find the GCF.
Step 1: List the factors of each coefficient: 4 (1, 2, 4), 18 (1, 2, 3, 6, 9, 18), 12 (1, 2, 3, 4, 6, 12)
Step 2: Find the largest common factor among these lists, which is 2
Step 1:
Step 2:
Math Tutor suggests: Practice Finding GCF and Factoring Expressions
Deepen your understanding of greatest common factor (GCF) and factoring with these related math questions and exercises.
FAQ on Finding the Greatest Common Factor
Can a variable be included in the GCF if all terms do not contain it?
No, a variable is only part of the GCF if it is present in every term.
What if all coefficients are even numbers?
The GCF will always at least include 2 if all coefficients are even numbers.
Why isn't 'k' included in the GCF for this question?
Because the term 12 does not have the variable k, so it cannot be part of the GCF.
Can the GCF be greater than the smallest coefficient?
No, the GCF cannot be larger than the smallest number involved.
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