High School

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Which of the following factor trees for 126 is correct?

A. 126
3 48
8 6
2 2 3 2

B. 126
7 18
2 3

C. 126
3 42
6 7
2 3

D. 126
7 18
3 6
3 3

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.

  1. Start with 126: It's even, so divide by 2.
    [tex]126 \div 2 = 63[/tex]

  2. Move to 63: Check the next smallest prime, which is 3.
    [tex]63 \div 3 = 21[/tex]

  3. Now with 21: Again, divide by 3.
    [tex]21 \div 3 = 7[/tex]

  4. 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

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