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Answer :
To find the prime factorization of 147, we need to write it as a product of its prime factors. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
Let's break down 147 into its prime factors:
1. Start with the smallest prime number, which is 2. Since 147 is an odd number, it is not divisible by 2.
2. Next, try the next smallest prime number, which is 3. Check if 147 is divisible by 3.
- Add the digits of 147: 1 + 4 + 7 = 12.
- 12 is divisible by 3, so 147 is also divisible by 3.
- Divide 147 by 3: 147 ÷ 3 = 49.
3. Now, we need to factor 49.
- Since 49 is not divisible by 3, we move to the next prime number, which is 5. But 49 does not end in 0 or 5, so it is not divisible by 5.
- Then, try the next prime number, which is 7.
- 49 is divisible by 7 because 49 ÷ 7 = 7.
4. We see that 7 is a prime number. Therefore, 49 can be factored as 7 × 7.
Now, we have completely factored 147 using prime numbers:
- 147 = 3 × 49
- 49 = 7 × 7
Therefore, the prime factorization of 147 is:
[tex]\[ 3 \times 7 \times 7 \][/tex]
The correct choice from the options provided is [tex]\( 3 \times 7 \times 7 \)[/tex].
Let's break down 147 into its prime factors:
1. Start with the smallest prime number, which is 2. Since 147 is an odd number, it is not divisible by 2.
2. Next, try the next smallest prime number, which is 3. Check if 147 is divisible by 3.
- Add the digits of 147: 1 + 4 + 7 = 12.
- 12 is divisible by 3, so 147 is also divisible by 3.
- Divide 147 by 3: 147 ÷ 3 = 49.
3. Now, we need to factor 49.
- Since 49 is not divisible by 3, we move to the next prime number, which is 5. But 49 does not end in 0 or 5, so it is not divisible by 5.
- Then, try the next prime number, which is 7.
- 49 is divisible by 7 because 49 ÷ 7 = 7.
4. We see that 7 is a prime number. Therefore, 49 can be factored as 7 × 7.
Now, we have completely factored 147 using prime numbers:
- 147 = 3 × 49
- 49 = 7 × 7
Therefore, the prime factorization of 147 is:
[tex]\[ 3 \times 7 \times 7 \][/tex]
The correct choice from the options provided is [tex]\( 3 \times 7 \times 7 \)[/tex].
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