The product of two consecutive positive even numbers is 728. What are the numbers? (Enter solutions from smallest to largest.)
and
Hint:
The square root of 728 is 26.98
Take it from there.
To find the consecutive positive even numbers whose product is 728, we can start by looking at the prime factorization of 728:
The prime factorization of 728 is 2^3 * 7^2.
Since we are looking for even numbers, we know that both numbers must be divisible by 2. Therefore, we can start by dividing the prime factorization of 728 by 2:
(2^3 * 7^2) / 2 = 2^2 * 7^2
Now, we have two prime factors left - 2^2 and 7^2. The product of the two consecutive positive even numbers must equal this remaining factorization.
The two possible combinations are:
- (2^2 * 7) * (7)
- (2^2) * (7^2)
Simplifying each combination, we find:
- (4 * 7) * (7) = 28 * 7 = 196
- (4) * (49) = 4 * 49 = 196
Therefore, the consecutive positive even numbers whose product is 728 are 28 and 26.