Question

Four different numbers are factorised
into prime factors. It is observed that
each of the numbers has prime factors
2, 3 & 5. Using the numbers of prime
factors 2, 3 & 5, Which of the following
number will be perfect cube ?
(1) 2 repeats 3 times, 3 repeats 3 times and
5 repeats 2 times.
(2) 2 occurs 4 times, 3 occurs 3 times and 5
occurs 3 times.
(3) 2 occurs 3 times, 3 occurs 1 time and 5
occurs 3 times.
(4) 2 occurs 3 times, 3 occurs 3 times and 5
occurs 3 times.​

Answer 1

Answer:

2700

Step-by-step explanation:

(1) 2 repeats 3 times, 3 repeats 3 times and  5 repeats 2 times.

2³3³5²- not a perfect cube because 5 has power 2

(2) 2 occurs 4 times, 3 occurs 3 times and 5  occurs 3 times.

2⁴3³5³- not a perfect cube because 2 has power 4

(3) 2 occurs 3 times, 3 occurs 1 time and 5  occurs 3 times.

2³35³- not a perfect cube because 3 has power 1

(4) 2 occurs 3 times, 3 occurs 3 times and 5  occurs 3 times.​

2³3³5³ = (2*3*5)³ - is a perfect cube

30³=2700