Question
- What is the greatest common factor of 48 and 64 ? * 3 points
Ask by Pena Lawson. in the United States
Dec 26,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The greatest common factor of 48 and 64 is 16.
Solution
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The Deep Dive
The greatest common factor (GCF) of 48 and 64 is 16. To find the GCF, you can list the factors of each number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, while the factors of 64 are 1, 2, 4, 8, 16, 32, and 64. The largest factor they have in common is 16!
To better understand how to determine the GCF, you can use the prime factorization method. For 48, the prime factors are 2 × 2 × 2 × 2 × 3 (or 2^4 × 3) and for 64, the prime factors are 2 × 2 × 2 × 2 × 2 × 2 (or 2^6). The GCF is found by taking the lowest power of each prime factor present in both numbers, which leads us again to 16 (2^4)!
