Question

Express the prime factorization of 1200 as a product of prime number with exponets

Answer 1

To express the prime factorization of 1200, we first factor it down into its prime numbers.

1. Start by dividing by the smallest prime number, which is 2:

\( 1200 \div 2 = 600 \)

2. Continue dividing by 2:

\( 600 \div 2 = 300 \)

3. Divide by 2 again:

\( 300 \div 2 = 150 \)

4. Divide by 2 once more:

\( 150 \div 2 = 75 \)

5. Now switch to the next smallest prime number, which is 3:

\( 75 \div 3 = 25 \)

6. Next, divide by 5 (the next prime number):

\( 25 \div 5 = 5 \)

7. Finally, divide by 5 once more:

\( 5 \div 5 = 1 \)

Now we can summarize the prime factorization:

- The prime factorization is:

\( 1200 = 2^4 \times 3^1 \times 5^2 \)

Thus, the prime factorization of 1200 as a product of prime numbers with exponents is:

\[ 1200 = 2^4 \times 3^1 \times 5^2 \]