2016 · Q32
What is the maximum value of m, if the number N = 90 x 42 x 324 x 55 is divisible by 3ᵐ?
Elementary MathematicsNumber System
- A8
- B7
- C6
- D5
Explanation
Counting factors of 3: 90 = 2·3²·5, 42 = 2·3·7, 324 = 2²·3⁴ and 55 = 5·11. Altogether N contains 3^{2+1+4} = 3⁷. No higher power of 3 divides N, so the maximum m is 7, option B.