Q58 / 160 · TS EAMCET 2024 (11 May Shift 1) · Mathematics

Number of ways in which the number 831600 can be split into two factors which are relatively prime is

  • A
    $8$
  • B
    $64$
  • C
    $32$
  • Correct answer
    D
    $16$

Solution

$831600=2^4 \times 3^3 \times 5^2 \times 7 \times 11$ $2^4$ can be a factor of one of the 2 factors. Similarly $3^3, 5^2, 7,11$. Required number $=\frac{2 \times 2 \times 2 \times 2 \times 2}{2!}=16$

Hence, the correct answer is option: 'D'.

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