Given S= (x, y, z) R^3 : xyz=210, x<y<z, where x, y, z are positive integers What is the total number of elements in S?

NDA 2026 Mathematics question

Given where are positive integers What is the total number of elements in ?

(A)10
(B)12
(C)13Correct
(D)More than 13

Answer: (C)

Solution

. Each of the 4 primes can go to any one of , giving ordered triples with product 210. Triples with two equal entries need a repeated square factor; since 210 is

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Question ID VK-030396