Answer :
Sure! Let's find the prime factorization of 76 through steps.
1. Check if 76 is divisible by 2:
Since 76 is an even number, it's divisible by 2. Divide 76 by 2:
[tex]\[
76 \div 2 = 38
\][/tex]
2. Continue with the result 38:
Again, 38 is an even number, so it's also divisible by 2. Divide 38 by 2:
[tex]\[
38 \div 2 = 19
\][/tex]
3. Check the result 19:
The number 19 is a prime number, meaning it cannot be divided by any number other than 1 and itself.
4. Combine the factors:
From the divisions above, we see that 76 can be expressed as:
[tex]\[
76 = 2 \times 2 \times 19
\][/tex]
5. Express using exponents:
Since 2 is used twice, we can write this using exponents:
[tex]\[
2^2 \times 19
\][/tex]
Thus, the prime factorization of 76 is [tex]\(2^2 \cdot 19\)[/tex].
1. Check if 76 is divisible by 2:
Since 76 is an even number, it's divisible by 2. Divide 76 by 2:
[tex]\[
76 \div 2 = 38
\][/tex]
2. Continue with the result 38:
Again, 38 is an even number, so it's also divisible by 2. Divide 38 by 2:
[tex]\[
38 \div 2 = 19
\][/tex]
3. Check the result 19:
The number 19 is a prime number, meaning it cannot be divided by any number other than 1 and itself.
4. Combine the factors:
From the divisions above, we see that 76 can be expressed as:
[tex]\[
76 = 2 \times 2 \times 19
\][/tex]
5. Express using exponents:
Since 2 is used twice, we can write this using exponents:
[tex]\[
2^2 \times 19
\][/tex]
Thus, the prime factorization of 76 is [tex]\(2^2 \cdot 19\)[/tex].
