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20 Mar 2024, 12:48
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
100% (00:43) correct
0% (00:00) wrong based on 3 sessions
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Which of the following numbers has more than two distinct prime factors? Indicate all such numbers.
A. 20
B. 30
C. 100
D. 200
E. 210
A. 20
B. 30
C. 100
D. 200
E. 210
12 Apr 2024, 16:27
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A. 20 =\(2^2 * 5\) = 2 distinct prime factors
B. 30 = \(3 * 2 * 5\)= 3 distinct prime factors
C. 100 = \(2^2 * 5^2\)= 2 distinct prime factors
D. 200 = \(2^3 * 5^2\)= 2 distinct prime factors
E. 210 = \(3 * 7 * 2 * 5\) = 4 distinct prime factors
Only option B, E has more than 2 distinct prime factors
B. 30 = \(3 * 2 * 5\)= 3 distinct prime factors
C. 100 = \(2^2 * 5^2\)= 2 distinct prime factors
D. 200 = \(2^3 * 5^2\)= 2 distinct prime factors
E. 210 = \(3 * 7 * 2 * 5\) = 4 distinct prime factors
Only option B, E has more than 2 distinct prime factors
23 Jun 2024, 12:13
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Official Explanation
The question asks which numbers have more than two distinct prime factors. Start with 20 and break it down into prime factors: 2 × 2 × 5. Since 20 has only 2 distinct prime factors (2 and 5), (A) can be eliminated. Next, notice that 100 is just 20 × 5, so it has the same two distinct prime factors as 20. (C) can therefore be eliminated. Similarly, 200 is just 100 × 2, so 200 also has the same two distinct prime factors as 20 and 100. Eliminate (D). Now break down 30 into prime factors: 2 × 3 × 5. There are three distinct prime factors here, so (B) is one of the correct answers. Since 210 is 30 × 7, it has four distinct prime factors (2 × 3 × 5 × 7), so (E) is also one of the correct answers.
The question asks which numbers have more than two distinct prime factors. Start with 20 and break it down into prime factors: 2 × 2 × 5. Since 20 has only 2 distinct prime factors (2 and 5), (A) can be eliminated. Next, notice that 100 is just 20 × 5, so it has the same two distinct prime factors as 20. (C) can therefore be eliminated. Similarly, 200 is just 100 × 2, so 200 also has the same two distinct prime factors as 20 and 100. Eliminate (D). Now break down 30 into prime factors: 2 × 3 × 5. There are three distinct prime factors here, so (B) is one of the correct answers. Since 210 is 30 × 7, it has four distinct prime factors (2 × 3 × 5 × 7), so (E) is also one of the correct answers.
