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Find the smallest positive integer k such that 360k is a cube number.

User MagMax
by
4.6k points

2 Answers

2 votes

Answer:

k = 75

Explanation:

Factorize 360

360 = 36 * 10

= 2 * 2 * 3 * 3 * 2 * 5

As 360k is cube number, k = 3 * 5 * 5

k = 75

360k = 360 * 75 = 27000 is a perfect cube

User Hassan Jawed
by
4.2k points
2 votes

Answer: k = 75

Explanation:

360

36 10

∧ ∧

6 6 2 5

∧ ∧

2 3 2 3

Prime factorization of 360 is: 2³ · 3² · 5

Since we want a perfect cube, every number must be to the power of 3.

That means we need a 3 and 2 more 5s to make a cube

k = 3 × 5 × 5

= 75

User IGGt
by
4.2k points