Answer :
To find the prime factorization of 112, we can break it down into its prime factors step-by-step:
1. Start with the smallest prime number: Begin by checking if 112 is divisible by 2, which is the smallest prime number.
2. Divide by 2:
- 112 ÷ 2 = 56. Since 112 is even, it's divisible by 2. This process can continue until it's no longer divisible by 2.
3. Continue dividing by 2:
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
Now you have reached a point where 7 is no longer divisible by 2.
4. Move to the next prime number (3): Check if 7 is divisible by 3. It is not.
5. Next prime number (5): Check if 7 is divisible by 5. It is not.
6. Next prime number is 7: Notice that 7 is a prime number itself, so it ends the factorization here.
The process reveals that the only prime factors of 112 are 2 and 7. We divided by 2 a total of four times, and then multiplied by 7. Thus, the prime factorization of 112 is:
[tex]\[ 112 = 2^4 \times 7 \][/tex]
Therefore, the prime factorization of 112 is [tex]\( 2^4 \times 7 \)[/tex].
1. Start with the smallest prime number: Begin by checking if 112 is divisible by 2, which is the smallest prime number.
2. Divide by 2:
- 112 ÷ 2 = 56. Since 112 is even, it's divisible by 2. This process can continue until it's no longer divisible by 2.
3. Continue dividing by 2:
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
Now you have reached a point where 7 is no longer divisible by 2.
4. Move to the next prime number (3): Check if 7 is divisible by 3. It is not.
5. Next prime number (5): Check if 7 is divisible by 5. It is not.
6. Next prime number is 7: Notice that 7 is a prime number itself, so it ends the factorization here.
The process reveals that the only prime factors of 112 are 2 and 7. We divided by 2 a total of four times, and then multiplied by 7. Thus, the prime factorization of 112 is:
[tex]\[ 112 = 2^4 \times 7 \][/tex]
Therefore, the prime factorization of 112 is [tex]\( 2^4 \times 7 \)[/tex].
