Which of the following numbers has the greatest number of distinct prime factors?
A. 165
B. 192
C. 228
D. 330
E. 332
How will i get a prime factor? What should i first?
OA D
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Which of the following numbers
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This requires us to find the prime factorization of each answer choicelheiannie07 wrote:Which of the following numbers has the greatest number of distinct prime factors?
A. 165
B. 192
C. 228
D. 330
E. 332
A. 165 = (3)(5)(11) --- 3 distinct prime factors
B. 192 = (2)(2)(2)(2)(2)(2)(3) --- 2 distinct prime factors
C. 228 = (2)(2)(3)(19) --- 3 distinct prime factors
D. 330 = (2)(3)(5)(11) --- 4 distinct prime factors
E. 332 = (2)(2)(83) --- 2 distinct prime factors
Answer: D
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Last edited by Brent@GMATPrepNow on Sun Apr 01, 2018 5:39 am, edited 1 time in total.
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Hi lheiannie07,Which of the following numbers has the greatest number of distinct prime factors?
A. 165
B. 192
C. 228
D. 330
E. 332
How will i get a prime factor? What should i first?
OA D
Let's take a look at your question.
To find the greatest distinct prime factors we need to factorize all the numbers in the options.
Prime factors of 165 = 3 * 5 * 11
Distinct Prime factors of 165 = 3, 5, 11
165 has 3 distinct prime factors.
Prime factors of 192 = 2 * 2 * 2 * 2 * 2 * 2 * 3
Distinct prime factors of 912 = 2, 3
192 has 2 distinct prime factors.
Prime factors of 228 = 2 * 2 * 3 * 19
Distinct prime factors of 228 = 2, 3, 19
228 has 3 distinct prime factors.
Prime factors of 330 = 2 * 3 * 5 * 11
Distinct prime factors of 330 = 2, 3, 5, 11
330 has 4 distinct prime factors.
Prime factors of 332 = 2 * 2 * 83
Distinct prime factors = 2, 2, 83
332 has 3 distinct prime factors.
Therefore, 330 has the greatest number of distinct prime factors.
Option D is correct.
Hope this helps.
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We can express each answer choice as a product of its prime factors:BTGmoderatorDC wrote:Which of the following numbers has the greatest number of distinct prime factors?
A. 165
B. 192
C. 228
D. 330
E. 332
How will i get a prime factor? What should i first?
OA D
A) 165
165 = 5 x 33 = 5 x 11 x 3
165 has 3 distinct prime factors.
B) 192
192 = 8 x 24 = 8 x 8 x 3 = 2^6 x 3^1
192 has 2 distinct prime factors.
C) 228
228 = 4 x 57 = 2^2 x 3 x 19
228 has 3 distinct prime factors.
D) 330
330 = 10 x 33 = 2 x 3 x 5 x 11
330 has 4 distinct prime factors.
E) 332
332 = 4 x 83 = 2^2 x 83
332 has 2 distinct prime factors.
330 has the greatest number of distinct prime factors.
Answer: D
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