Maths · Arithmetic and Geometric progressions
Find the smallest number by which 26244 is divided to get the quotient as a perf
Find the smallest number by which 26244 is divided to get the quotient as a perfect cube
- A. 4
- B. 9
- C. 18
- D. 36 6
Step-by-step solution
Prime factorize 26244: 26244 = 2^2 × 3^8. For a perfect cube, all exponents must be multiples of 3. Divide by 2^2 = 4 to reduce exponent of 2 to 0 (multiple of 3), and by 3^2 = 9 to reduce exponent of 3 to 6 (multiple of 3). Thus, divide by 4 × 9 = 36. Check: 26244 ÷ 36 = 729 = 9^3, a perfect cube.
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