What is a greatest common factor (GCF)?Responseslargest number or quantity that divides evenly into all termslargest number or quantity that divides evenly into all termsa variable that when multiplied by another number or quantity results in a producta variable that when multiplied by another number or quantity results in a producta number or quantity that when multiplied by another number or quantity results in a product
Question
What is a greatest common factor (GCF)?Responseslargest number or quantity that divides evenly into all termslargest number or quantity that divides evenly into all termsa variable that when multiplied by another number or quantity results in a producta variable that when multiplied by another number or quantity results in a producta number or quantity that when multiplied by another number or quantity results in a product
Solution
The Greatest Common Factor (GCF) is the largest number that can evenly divide into all terms. In other words, it is the highest number that you can divide all of the numbers by without any remainder. It's used in simplifying or solving fractions and algebraic expressions.
Here's a step-by-step process to find the GCF:
- List the prime factors of each number.
- Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.
For example, let's find the GCF of 18 and 27:
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Prime factors of 18: 2, 3, 3 Prime factors of 27: 3, 3, 3
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The common factors are 3 and 3. So, the GCF is 3*3 = 9.
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