Answer :
To find the prime factorization of 126, we break it down into its prime components by dividing it by the smallest prime numbers. Here’s a step-by-step explanation:
1. Divide by 2:
- Since 126 is an even number, we start by dividing it by 2, the smallest prime number.
- [tex]\(126 \div 2 = 63\)[/tex]
- Now, 126 can be expressed as [tex]\(2 \times 63\)[/tex].
2. Divide by 3:
- The result, 63, is not even, so we try dividing it by 3, the next smallest prime.
- [tex]\(63 \div 3 = 21\)[/tex]
- So, 63 can be expressed as [tex]\(3 \times 21\)[/tex].
3. Continue dividing by 3:
- Now, take the result 21 and divide it again by 3.
- [tex]\(21 \div 3 = 7\)[/tex]
- So, 21 can be expressed as [tex]\(3 \times 7\)[/tex].
4. Final factorization with 7:
- The result 7 is a prime number.
- We don’t need to divide further since 7 can't be divided by any number other than 1 and itself.
Combining all the steps, we find that the prime factorization of 126 is [tex]\(2 \times 3 \times 3 \times 7\)[/tex], which can also be written as [tex]\(2 \times 3^2 \times 7\)[/tex].
1. Divide by 2:
- Since 126 is an even number, we start by dividing it by 2, the smallest prime number.
- [tex]\(126 \div 2 = 63\)[/tex]
- Now, 126 can be expressed as [tex]\(2 \times 63\)[/tex].
2. Divide by 3:
- The result, 63, is not even, so we try dividing it by 3, the next smallest prime.
- [tex]\(63 \div 3 = 21\)[/tex]
- So, 63 can be expressed as [tex]\(3 \times 21\)[/tex].
3. Continue dividing by 3:
- Now, take the result 21 and divide it again by 3.
- [tex]\(21 \div 3 = 7\)[/tex]
- So, 21 can be expressed as [tex]\(3 \times 7\)[/tex].
4. Final factorization with 7:
- The result 7 is a prime number.
- We don’t need to divide further since 7 can't be divided by any number other than 1 and itself.
Combining all the steps, we find that the prime factorization of 126 is [tex]\(2 \times 3 \times 3 \times 7\)[/tex], which can also be written as [tex]\(2 \times 3^2 \times 7\)[/tex].
