Final answer:
The greatest common divider of 6³ and 3⁶ is 3³.
Step-by-step explanation:
To find the greatest common divider of 6³ and 3⁶, we need to factorize the numbers. 6³ can be written as 2³ * 3³ and 3⁶ can be written as (3³)². The common factor between the two numbers is 3³, so the answer is 3³.
The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCD of 6³ (6 x 6 x 6) and 3¶ (3 x 3 x 3 x 3 x 3 x 3), we need to break each number down to its prime factors.
6³ can be expressed as (3 x 2)³, which is 3³ x 2³, and 3¶ is simply 3 multiplied by itself six times. The common factor in both expressions is 3³, since 3¶ contains 3³ within it, and 6³ only goes as far as 3³. Therefore, the GCD of 6³ and 3¶ is 3³. The answer is A) 3³.