Question

How many positive cubes divide 3! x 5! x 7!?
(A) 2
(B) 3
(C) 4
(D) 6
Correct Answer with Solution will be Marked Brainliest ​

Answer 1

For a natural number to be a cube, each factor must be a cube. Our number is [Math Processing Error]3!5!7!=28⋅34⋅52⋅7.

Here we will divide the number into prime factors, the only possibilities will be prime factors with an exponent divisible by 3. So, you can freely omit the factors [Math Processing Error]52,7 and this "remainder" of [Math Processing Error]28 and [Math Processing Error]34 from the observation, i.e. we are only looking at combinations of factors 26 and

correct option is d no 6