What is the median of all possible factors of 120?
Answer
Correct Answer : b ) 11
Explanation :Let us first find the prime factorization of 120
120 = 2 x 2 x 2 x 3 x 5 = 23.3.5
Total number of factors of 120 = (3 + 1).(1 + 1).(1 + 1) = 4 x 2 x 2 = 16
The possible factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, .......
Median of all possible factors of 120 = Mean of 16/2 th and (16/2 + 1) th factor when written in ascending order.
Median of all possible factors of 120 = Mean of 8th and 9th factor when written in ascending order.
Median of all possible factors of 120 = (10 + 12)/2 = 11
Hence, (b) is the correct answer.
This question was asked in UPSC CDS Exam 2 2022.
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