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04 Feb 2022, 07:45
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Set A consists of the prime factors of the number 22680. If each number in Set A is repeated the same number of times as it appears in the full prime factorization of 22680, what is the mode of Set A?
A. 2
B. 3
C. 5
D. 7
E. 8
A. 2
B. 3
C. 5
D. 7
E. 8
04 Feb 2022, 07:58
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The question as worded doesn't describe what it's trying to describe, because the "set" it mentions does not "consist of the prime factors of 22680", if the primes are repeated several times. The set "consisting of the prime factors of 22680" is the set {2, 3, 5, 7}.
They mean to ask which prime will have the highest exponent in the prime factorization of 22,680 = (10)(2268) = (5)(2)(2268) = (5)(4536) = (5)(9)(504) = (5)(9)(9)(56) = (2^3)(3^4)(5)(7), and the answer is '3'.
They mean to ask which prime will have the highest exponent in the prime factorization of 22,680 = (10)(2268) = (5)(2)(2268) = (5)(4536) = (5)(9)(504) = (5)(9)(9)(56) = (2^3)(3^4)(5)(7), and the answer is '3'.
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04 Feb 2022, 12:27
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To solve this exercise we must decompose the number 22680 into prime factors and choose the one that is repeated the most.
To form the set A, we must obtain the prime factors of 22680.
If we decompose 22680, we obtain 2exp3 x 3exp4 x 5exp1 x 7exp1, then the mode of set A is 3, since it is the prime factor, which appears the most times in set A.
Answer B
To form the set A, we must obtain the prime factors of 22680.
If we decompose 22680, we obtain 2exp3 x 3exp4 x 5exp1 x 7exp1, then the mode of set A is 3, since it is the prime factor, which appears the most times in set A.
Answer B
