Question

What is the prime factorization of 1200 as a product of prime numbers with exponents

Answer 1

The prime factorization of 1200 is 2^4 × 3 × 5^2.

Step-by-step explanation:

The prime factorization of 1200 can be found by dividing the number by prime numbers until we cannot divide anymore. Here is the step-by-step process:

1. Start by dividing 1200 by the smallest prime number, which is 2. We get 600 as the quotient.
2. Now, continue dividing 600 by 2. We get 300 as the quotient.
3. Divide 300 by 2 again to get 150 as the quotient.
4. Divide 150 by 2 one more time to get 75.
5. Now, the number is no longer divisible by 2. So, move on to the next prime number, which is 3. Divide 75 by 3 to get 25.
6. Finally, divide 25 by 5 to get 5.

Therefore, the prime factorization of 1200 is 2^4 × 3 × 5^2.