Let's analyze the statements one by one regarding the numbers 63 and 20:
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They are both prime numbers.
- This statement is false. A prime number has exactly two distinct positive divisors: 1 and itself.
- 63 is not a prime number because it can be divided by 1, 3, 7, 9, 21, and 63.
- 20 is not a prime number either since it can be divided by 1, 2, 4, 5, 10, and 20.
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They have more than one common factor.
- This statement is false. The common factors of 63 and 20 are only 1. Since 1 is the only common factor, they do not have more than one common factor.
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They are relatively prime.
- This statement is true. Two numbers are relatively prime if their greatest common divisor (GCD) is 1. Since the only common factor is 1, 63 and 20 are relatively prime.
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They each have a factor of 4.
- This statement is false. While 20 has a factor of 4 (since 20 = 4 × 5), 63 does not (since 63 is not divisible by 4).
Based on the analysis, the correct statement is: They are relatively prime.