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7:23 174 Done deltamath.com (!) This is the only question in this section. Question Video Examples What is the prime factorization of \( 147 ? \) Use the \( \times \) button or type the * key on your keyboard. For exponents, use the \( a^{b} \) button or the \( { }^{\wedge} \) key on your keyboard. If a number is prime, enter the number itself. Answer Attempt 1 out of 2 \[ 147=\square \times \sqrt[a]{a^{b}} \] Submit Answer
Ask by Chadwick Grant. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The prime factorization of \(147\) is \(3 \times 7^{2}\).
Solution
To find the prime factorization of \(147\), follow these steps:
1. **Divide by the smallest prime number (3):**
\[
147 \div 3 = 49
\]
2. **Factorize 49:**
\[
49 = 7 \times 7 = 7^2
\]
So, the prime factorization of \(147\) is:
\[
147 = 3 \times 7^{2}
\]
**Final Answer:**
\[
147 = 3 \times 7^{2}
\]
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Simplify this solution Bonus Knowledge
To find the prime factorization of 147, start by dividing it by the smallest prime number, which is 3. Since \( 147 \div 3 = 49 \), we have one factor. Next, break down 49, which is \( 7 \times 7 \). So, the prime factorization of 147 is \( 3 \times 7^2 \). If you're ever stuck on prime factorization, a great tip is to use a factor tree! Start with the number at the top and break it down into its factors step by step. Just keep dividing by the smallest prime numbers until you only have primes left. It's a fun visual way to see how numbers break down!
