Answer :
Sure, let's perform the prime factorization of 50 and 100 step-by-step.
### Prime Factorization of 50
1. Divide by the smallest prime number (2):
[tex]\[
50 \div 2 = 25
\][/tex]
So, 2 is one of the prime factors.
2. Divide the remaining number (25) by the smallest prime number not greater than 25:
[tex]\[
25 \div 5 = 5
\][/tex]
So, 5 is another prime factor, but we need to continue factoring 25.
3. Divide the remaining number (5) by the smallest prime number (5):
[tex]\[
5 \div 5 = 1
\][/tex]
So, we have factored 50 completely.
The prime factorization of 50 is:
[tex]\[
50 = 2^1 \times 5^2
\][/tex]
### Prime Factorization of 100
1. Divide by the smallest prime number (2):
[tex]\[
100 \div 2 = 50
\][/tex]
So, 2 is one of the prime factors.
2. Divide the remaining number (50) by the smallest prime number (2):
[tex]\[
50 \div 2 = 25
\][/tex]
So, another 2 is a prime factor.
3. Divide the remaining number (25) by the smallest prime number not greater than 25:
[tex]\[
25 \div 5 = 5
\][/tex]
So, 5 is another prime factor, but we need to continue factoring 25.
4. Divide the remaining number (5) by the smallest prime number (5):
[tex]\[
5 \div 5 = 1
\][/tex]
So, we have factored 100 completely.
The prime factorization of 100 is:
[tex]\[
100 = 2^2 \times 5^2
\][/tex]
So, summarizing the prime factorization results:
- Prime factors of 50: [tex]\[2, 5\][/tex]
- Complete factorization of 50: [tex]\[50 = 2^1 \times 5^2\][/tex]
- Prime factors of 100: [tex]\[2, 5\][/tex]
- Complete factorization of 100: [tex]\[100 = 2^2 \times 5^2\][/tex]
### Prime Factorization of 50
1. Divide by the smallest prime number (2):
[tex]\[
50 \div 2 = 25
\][/tex]
So, 2 is one of the prime factors.
2. Divide the remaining number (25) by the smallest prime number not greater than 25:
[tex]\[
25 \div 5 = 5
\][/tex]
So, 5 is another prime factor, but we need to continue factoring 25.
3. Divide the remaining number (5) by the smallest prime number (5):
[tex]\[
5 \div 5 = 1
\][/tex]
So, we have factored 50 completely.
The prime factorization of 50 is:
[tex]\[
50 = 2^1 \times 5^2
\][/tex]
### Prime Factorization of 100
1. Divide by the smallest prime number (2):
[tex]\[
100 \div 2 = 50
\][/tex]
So, 2 is one of the prime factors.
2. Divide the remaining number (50) by the smallest prime number (2):
[tex]\[
50 \div 2 = 25
\][/tex]
So, another 2 is a prime factor.
3. Divide the remaining number (25) by the smallest prime number not greater than 25:
[tex]\[
25 \div 5 = 5
\][/tex]
So, 5 is another prime factor, but we need to continue factoring 25.
4. Divide the remaining number (5) by the smallest prime number (5):
[tex]\[
5 \div 5 = 1
\][/tex]
So, we have factored 100 completely.
The prime factorization of 100 is:
[tex]\[
100 = 2^2 \times 5^2
\][/tex]
So, summarizing the prime factorization results:
- Prime factors of 50: [tex]\[2, 5\][/tex]
- Complete factorization of 50: [tex]\[50 = 2^1 \times 5^2\][/tex]
- Prime factors of 100: [tex]\[2, 5\][/tex]
- Complete factorization of 100: [tex]\[100 = 2^2 \times 5^2\][/tex]