Answer :

To find the prime factorization of 76, follow these steps:

1. Start with the smallest prime number, which is 2.

Check if 76 is divisible by 2. Since 76 is an even number, it is divisible by 2.

[tex]\[
76 \div 2 = 38
\][/tex]

So, 2 is a factor, and 38 is the quotient.

2. Continue dividing by 2 to find more factors of 2 if possible.

Next, check if 38 is still divisible by 2. Since 38 is also an even number, divide by 2 again:

[tex]\[
38 \div 2 = 19
\][/tex]

So, another factor of 2 is found, leaving 19 as the quotient.

3. Check if the quotient (19) is a prime number.

Now, we have 19 remaining. Check if 19 is a prime number by testing it for divisibility by any prime numbers smaller than or equal to its square root. Since 19 is not divisible by any of these numbers, 19 is indeed a prime number.

Therefore, the prime factors of 76 are two 2's and one 19.

The prime factorization of 76 is:

[tex]\[
76 = 2 \times 2 \times 19
\][/tex]

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