Answer :
To determine which factor tree for 126 is correct, we need to break down 126 into its prime factors step-by-step by dividing it by prime numbers.
Start with 126: It's even, so divide by 2.
[tex]126 \div 2 = 63[/tex]Move to 63: Check the next smallest prime, which is 3.
[tex]63 \div 3 = 21[/tex]Now with 21: Again, divide by 3.
[tex]21 \div 3 = 7[/tex]Lastly, we have 7: 7 is a prime number, so it cannot be divided further.
Thus, the prime factorization of 126 is:
[tex]126 = 2 \times 3^2 \times 7[/tex]
Now, let's look at the options provided:
Option A: 126 3 48 8 6 2 2 3 2
- This does not fit our factor tree or factorization.
Option B: 126 7 18 2 3
- This does fit, because the breakdown would be 126 divided to give the factors 7, 18, which further breaks down as 18 to factors 2 and 3².
Option C: 126 3 42 6 7 2 3
- This gives the factorization, as the sequence starts 126 divided by 3, yielding 42, which breaks down similarly.
Option D: 126 7 18 3 6 3 3
- This shows incorrect calculations in division steps.
Thus, both options B and C correctly represent different paths of the factorization for the number 126. But going through exact prime factors sequence, Option C is correct.
Correct Option: C
