Question
What is the GCF of 12 and 20 ? \( \square \) \( \square \)
Ask by George Osborne. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The greatest common factor of 12 and 20 is 4.
Solution
1. Write the prime factorizations:
- \( 12 = 2^2 \times 3 \)
- \( 20 = 2^2 \times 5 \)
2. Identify the common prime factors. Both numbers have the factor \( 2^2 \).
3. Multiply the common factors to obtain the GCF:
\[
\text{GCF} = 2^2 = 4
\]
Thus, the greatest common factor is:
\[
\boxed{4}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
The greatest common factor (GCF) of 12 and 20 is 4! This means that 4 is the largest number that divides both 12 and 20 without leaving a remainder. You can find the GCF by listing the factors: the factors of 12 are 1, 2, 3, 4, 6, and 12; and the factors of 20 are 1, 2, 4, 5, 10, and 20. The highest common factor in both lists is 4! To visualize this concept, think of it as finding the biggest pizza that two friends can equally share. If one friend has a 12-slice pizza and the other has a 20-slice pizza, they can only share slices of 4 at a time without anyone getting shortchanged. So, get ready to slice up that pizza with your GCF skills! 🍕
