To determine the largest prime factor of 12, we need to perform the prime factorization of the number. Here is a step-by-step breakdown:
1. Identify Prime Numbers:
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. Examples include 2, 3, 5, 7, 11, etc.
2. Find the Prime Factors of 12:
Start dividing 12 by the smallest prime number, which is 2:
[tex]\[
12 \div 2 = 6
\][/tex]
So, 2 is a prime factor, and we continue with the quotient, 6.
Next, divide 6 by 2:
[tex]\[
6 \div 2 = 3
\][/tex]
So, another 2 is a prime factor, and we continue with the quotient, 3.
Now, 3 is a prime number and cannot be divided further by any number other than 1 and itself:
[tex]\[
3 \div 3 = 1
\][/tex]
So, 3 is a prime factor.
3. List the Prime Factors:
By performing these divisions, we find that the prime factors of 12 are:
[tex]\[
12 = 2 \times 2 \times 3
\][/tex]
4. Determine the Largest Prime Factor:
From the list of prime factors (2, 2, 3), the largest prime number is:
[tex]\[
3
\][/tex]
Therefore, the largest prime factor of 12 is [tex]\( \boxed{3} \)[/tex].
