To reduce the number 27 to its prime factors, we need to identify the prime numbers that multiply together to give us 27.
1. Identify the smallest prime factor:
- The smallest prime number that divides into 27 is 3.
2. Divide 27 by this prime factor:
- Dividing 27 by 3 gives us 9. So, one factor is 3.
[tex]\[
27 \div 3 = 9
\][/tex]
3. Repeat the process with the quotient:
- The quotient is 9. The smallest prime number that divides into 9 is again 3.
[tex]\[
9 \div 3 = 3
\][/tex]
4. Repeat the process again:
- The quotient is 3. The smallest prime number that divides 3 is 3.
[tex]\[
3 \div 3 = 1
\][/tex]
Now we have completely factored 27 into prime factors, and repeatedly dividing by 3 yields 1.
5. Combine the prime factors:
- We can write 27 as a product of prime numbers. From the steps above, we see that 27 is [tex]\( 3 \times 3 \times 3 \)[/tex].
6. Express in exponential form:
- To express 27 in exponential form, we note that [tex]\(\ 3 \)[/tex] is used as a factor 3 times. Thus, we can write:
[tex]\[
27 = 3^3
\][/tex]
This indicates that the prime factorization of 27 is [tex]\( 3^3 \)[/tex]. So, we have reduced 27 to its prime factors and expressed it in the simplest form as [tex]\( 3^3 \)[/tex].
Therefore, the final result is:
[tex]\[ 27 = 3^3 \][/tex]
