Final answer:
The perfect square factors of 792 are 4, 9, and 36. They are obtained through the prime factorization of 792, which is 2³ × 3² × 11, by combining the prime factors to form perfect squares.
Step-by-step explanation:
To find the perfect square factors of 792, we need to factorize 792 and look for squares among its factors. First, let's find the prime factorization of 792. We start by dividing by the smallest prime, which is 2:
- 792 ÷ 2 = 396
- 396 ÷ 2 = 198
- 198 ÷ 2 = 99
- 99 can be divided by 3: 99 ÷ 3 = 33
- 33 ÷ 3 = 11
- 11 is a prime number, so we stop here.
So, the prime factorization of 792 is 2³ × 3² × 11. Now, to find the perfect square factors, we need to look for combinations of these prime factors that will result in perfect squares. The perfect squares from the prime factors of 792 are 4 (which is 2²), 9 (which is 3²), and 36 (which is 2² × 3²).
The perfect square factors of 792 in ascending order are: 4, 9, 36.