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