Question

Find the least number must be multiplied with 3456 such that the product a perfect cube

Answer 1

Hi there!
Here's the answer:

•°•°•°•°•°<><><<><>>•°•°•°•°•°•

¶ Type of problem
To find the least No. that should be multiplied to No. x so that the resultant product is a perfect cube.

•°•°•°•°•°<><><<><>><><>•°•°•°•°•°

¶ Approach to problem
Steps:
• Resolve the given number x into product of prime factors
• Express the number x as product of prime factors in exponential form.
• The least number that should be multiplied to number x is the prime factor(s) that is(are) not having 3 as their power.

•°•°•°•°•°•<><><<><>>•°•°•°•°•°

Now,
given No. = 3456

2 | 3456
2 | 1728
2 | 864
2 | 432
2 | 216
2 | 108
2 | 54
3 | 27
3 | 3
• | 1

7803 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

In exponential form,
7803 = 2³ × 2³ × 3³ × 2

Here, the number 2 is not having 3 as its power.
•°• The number 7803 is to be multiplied by 3 to make it a perfect cube


•°• Required least No. = 2

•°•°•°•°•°•<><><<><>>•°•°•°•°•°


©#£€®$


:)



Hope it helps