Answer :
To find the prime factorization of the composite number 114, we need to break it down into its prime factors. Here is the step-by-step process for factorizing 114:
1. Check for divisibility by 2:
- Since 114 is an even number, it is divisible by 2.
- Dividing 114 by 2 gives us 57:
[tex]\[
114 \div 2 = 57
\][/tex]
- So, we have:
[tex]\[
114 = 2 \times 57
\][/tex]
2. Check for divisibility by 3:
- Next, we check if 57 is divisible by 3. To do this, we sum the digits of 57 (5 + 7 = 12) and see if the result is divisible by 3.
- Since 12 is divisible by 3, 57 is also divisible by 3.
- Dividing 57 by 3 gives us 19:
[tex]\[
57 \div 3 = 19
\][/tex]
- So, we have:
[tex]\[
114 = 2 \times 3 \times 19
\][/tex]
3. Check if 19 is a prime number:
- The number 19 is a prime number because it is only divisible by 1 and itself.
Thus, the prime factorization of 114 is:
[tex]\[
114 = 2 \times 3 \times 19
\][/tex]
So, the prime factors of 114 are [tex]\(2, 3,\)[/tex] and [tex]\(19\)[/tex].
1. Check for divisibility by 2:
- Since 114 is an even number, it is divisible by 2.
- Dividing 114 by 2 gives us 57:
[tex]\[
114 \div 2 = 57
\][/tex]
- So, we have:
[tex]\[
114 = 2 \times 57
\][/tex]
2. Check for divisibility by 3:
- Next, we check if 57 is divisible by 3. To do this, we sum the digits of 57 (5 + 7 = 12) and see if the result is divisible by 3.
- Since 12 is divisible by 3, 57 is also divisible by 3.
- Dividing 57 by 3 gives us 19:
[tex]\[
57 \div 3 = 19
\][/tex]
- So, we have:
[tex]\[
114 = 2 \times 3 \times 19
\][/tex]
3. Check if 19 is a prime number:
- The number 19 is a prime number because it is only divisible by 1 and itself.
Thus, the prime factorization of 114 is:
[tex]\[
114 = 2 \times 3 \times 19
\][/tex]
So, the prime factors of 114 are [tex]\(2, 3,\)[/tex] and [tex]\(19\)[/tex].
