Question
Write 36 as a product of prime factors.
In your answer, write each prime factor that appears more than once using an exponent.
In your answer, write each prime factor that appears more than once using an exponent.
Answers
GPT-4o mini
To express 36 as a product of its prime factors, we can start by dividing it by the smallest prime numbers.
1. Divide by 2:
\[
36 \div 2 = 18
\]
2. Divide 18 by 2 again:
\[
18 \div 2 = 9
\]
3. Now, divide 9 by the next smallest prime number, which is 3:
\[
9 \div 3 = 3
\]
4. Finally, divide 3 by 3:
\[
3 \div 3 = 1
\]
We can gather all the prime factors obtained from the divisions:
- From the first step, we have two factors of 2.
- From the last two steps, we have two factors of 3.
Therefore, we can write 36 as:
\[
36 = 2^2 \times 3^2
\]
Thus, the prime factorization of 36 is:
\[
\boxed{2^2 \times 3^2}
\]
1. Divide by 2:
\[
36 \div 2 = 18
\]
2. Divide 18 by 2 again:
\[
18 \div 2 = 9
\]
3. Now, divide 9 by the next smallest prime number, which is 3:
\[
9 \div 3 = 3
\]
4. Finally, divide 3 by 3:
\[
3 \div 3 = 1
\]
We can gather all the prime factors obtained from the divisions:
- From the first step, we have two factors of 2.
- From the last two steps, we have two factors of 3.
Therefore, we can write 36 as:
\[
36 = 2^2 \times 3^2
\]
Thus, the prime factorization of 36 is:
\[
\boxed{2^2 \times 3^2}
\]