Question

If 600 can be written as 2^a * b * c^d, where a, b, and c are prime numbers, what are the values of a, b, c, and d?

a. a = 3, b = 5, c = 2, d = 2
b. a = 2, b = 3, c = 5, d = 2
c. a = 2, b = 5, c = 3, d = 2
d. a = 3, b = 2, c = 5, d = 2

Answer 1

After prime factorization of 600, it is expressed as 2^3 * 5^2 * 3^1. This corresponds to the values a = 3, b = 5, c = 3, and d = 2; making the correct answer option c. a = 3, b = 5, c = 3, d = 2.

Step-by-step explanation:

The original question asks if 600 can be written as 2^a * b * c^d, where a, b, and c are prime numbers, what are the values of a, b, c, and d? To answer this, we must perform prime factorization on the number 600.

Firstly, we find that 600 is divisible by 2, which is a prime number. We continue dividing by 2 until we cannot anymore:

• 600 / 2 = 300
• 300 / 2 = 150
• 150 / 2 = 75

At this point, 75 is not divisible by 2. The next prime number to try is 3, but 75 is not divisible by 3 either. We move on to the next prime number, which is 5:

• 75 / 5 = 15
• 15 / 5 = 3

Finally, 3 is also a prime number and cannot be divided further. So we end up with the prime factors of 600 as 2, 2, 2 (which is 2^3), 5, 5 (which is 5^2), and 3. Therefore, our expression for 600 becomes 2^3 * 5^2 * 3^1.

Comparing this with the choices given, the correct answer is:

• a = 3
• b = 5
• c = 3
• d = 2

Thus the correct option is c. a = 3, b = 5, c = 3, d = 2.