Which expression represents the prime factorization of 129? A. 2 x 43 B. 3 x 43 C. 2 x 3 x 43 D. 3 x 3 x 43
The Correct Answer and Explanation is:
The correct answer is: B. 3 × 43
Explanation:
To find the prime factorization of 129, we need to break it down into its smallest prime number factors.
Start by testing the smallest prime numbers:
- Is 129 divisible by 2?
No. 129 is an odd number, so it is not divisible by 2. - Is 129 divisible by 3?
To check this, add the digits:
1 + 2 + 9 = 12
Since 12 is divisible by 3, 129 is divisible by 3.
Now divide 129 by 3:
129 ÷ 3 = 43 - Is 43 a prime number?
Yes. 43 is only divisible by 1 and itself. It is a prime number.
So, we can write:
129 = 3 × 43
This is the prime factorization of 129. There are no other prime factors because both 3 and 43 are primes. You cannot factor them further.
Let’s briefly check the other choices to confirm why they are incorrect:
- A. 2 × 43
This equals 86, not 129. - C. 2 × 3 × 43
This equals 2 × 129 = 258, which is too large. - D. 3 × 3 × 43
This equals 9 × 43 = 387, also too large.
Only 3 × 43 equals 129 exactly, and both numbers are prime. Therefore, the correct and complete prime factorization of 129 is 3 × 43, which matches option B.
