Question

Question
Express the prime factorization of 1,200 as a product of prime numbers with exponents.

Answer 1

To find the prime factorization of 1,200, we need to find the prime numbers that divide evenly into it.

First, we can divide 1,200 by 2:
1,200 ÷ 2 = 600

Next, we can divide 600 by 2 again:
600 ÷ 2 = 300

We can continue dividing by 2 until we can no longer divide evenly:

300 ÷ 2 = 150
150 ÷ 2 = 75

Now, we move on to the next prime number, which is 3. We divide 75 by 3:
75 ÷ 3 = 25

Now, we divide 25 by the next prime number, which is 5:
25 ÷ 5 = 5

Finally, we divide 5 by itself:
5 ÷ 5 = 1

Since we've reached 1, we have found all the prime factors. Therefore, the prime factorization of 1,200 is:

2^4 * 3 * 5