Praxis 5003 Practice Test Practice Question
The prime factorization of the number A is 2^3 * 5^2, and for the number B, it is 2^2 * 5^3. What is the greatest common factor of A and B?
Correct Answer: B
Rationale: To find the greatest common factor (GCF) of A and B, we look at the prime factorization of each number. For A, the prime factorization is \(2^3 \times 5^2\), and for B, it is \(2^2 \times 5^3\). The GCF is determined by taking the lowest power of each prime factor present in both numbers.
For the factor 2, the minimum power is \(2^2\). For the factor 5, the minimum power is \(5^2\). Therefore, the GCF is \(2^2 \times 5^2 = 4 \times 25 = 100\).
- Option A (10) is too low, as it does not account for the higher powers of both prime factors.
- Option C (50) is incorrect because it uses \(5^2\) but does not include the correct power of 2.
- Option D (100) reflects the correct calculation of the GCF based on the lowest powers of each prime factor.
Thus, the GCF of A and B is 100.
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