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 can start by dividing it by the smallest prime number, which is 2.

1,200 ÷ 2 = 600.

Now we divide 600 by 2 again:

600 ÷ 2 = 300.

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

300 ÷ 2 = 150.
150 ÷ 2 = 75.

Now we try the next prime number, which is 3:

75 ÷ 3 = 25.

After that, we try dividing by 5:

25 ÷ 5 = 5.

Finally, we're left with the prime number 5, which cannot be divided further.

The prime factorization of 1,200 can therefore be expressed as:

2² × 3 × 5².

So, the prime factorization of 1,200 as a product of prime numbers with exponents is 2² × 3 × 5².