Find the smallest number by which 192 must be divided to obtain a perfect cube.
Grade 8 Mathematics
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Prime factorization of 192
When 192 = (2²)³ × 3 is divided by 3, we get (2²)³ = 4³ = 64. ∴ 3 is the answer.
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Answer:
Smallest Number= 3
Step-by-step explanation:
Prime factorization of 192 = 2×2×2×2×2×2×3= 2^6×3 = (2^2)^3 ×3
192= (2^2)^3 ×3
3 is divided.
Then, we get =>(2^2)^3 = 4 ^3 = 4×4×4 = 64
Hence, 3 is the smallest no. by which 192 must be divided to obtain a perfect cube that is 64= 4^3
Hope it helps!
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