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If n is an integer and 210/n is an integer, which of the fo
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20 Jul 2020, 05:05
20 Jul 2020, 05:05
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If n is an integer and \(\frac{ 210}{n}\) is an integer, which of the following could be the value of n?
Indicate all such values.
A 6
B 12
C 14
D 35
E 42
Indicate all such values.
A 6
B 12
C 14
D 35
E 42
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Official Answer
A,C,D,E
Re: If n is an integer and 210/n is an integer, which of the fo
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20 Jul 2020, 05:05
20 Jul 2020, 05:05
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: If n is an integer and 210/n is an integer, which of the fo
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03 Aug 2020, 06:27
03 Aug 2020, 06:27
Carcass wrote:
If n is an integer and \(\frac{ 210}{n}\) is an integer, which of the following could be the value of n?
Indicate all such values.
A 6
B 12
C 14
D 35
E 42
Indicate all such values.
A 6
B 12
C 14
D 35
E 42
This question is asking us to find values of n that are divisors of 210
A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If k is a divisor of N, then k is "hiding" within the prime factorization of N
Consider these examples:
3 is a divisor of 24, because 24 = (2)(2)(2)(3), and we can clearly see the 3 hiding in the prime factorization.
Likewise, 5 is a divisor of 70 because 70 = (2)(5)(7)
And 8 is a divisor of 112 because 112 = (2)(2)(2)(2)(7)
And 15 is a divisor of 630 because 630 = (2)(3)(3)(5)(7)
-----BACK TO THE QUESTION!---------------------
210 = (2)(3)(5)(7)
A 6 = (2)(3)
210 = (2)(3)(5)(7)
So, 6 IS a divisor of 210
B 12 = (2)(2)(3)
210 = (2)(3)(5)(7)
Since 12 is NOT hiding in the prime factorization of 210, 12 is NOT a divisor of 210
C 14 = (2)(7)
210 = (2)(3)(5)(7)
So, 14 IS a divisor of 210
D 35 = (5)(7)
210 = (2)(3)(5)(7)
So, 35 IS a divisor of 210
E 42 = (2)(3)(7)
210 = (2)(3)(5)(7)
So, 42 IS a divisor of 210
Answer: A, C, D, E
