Question
2. Write 720 as a product of it's prime factors
Ask by Bush Coles. in Mozambique
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
720 can be written as \( 2^4 \times 3^2 \times 5 \).
Solution
To express **720** as a product of its prime factors, follow these steps:
1. **Divide by the smallest prime number (2):**
- \( 720 \div 2 = 360 \)
- \( 360 \div 2 = 180 \)
- \( 180 \div 2 = 90 \)
- \( 90 \div 2 = 45 \)
So, we have \( 2^4 \) (since we divided by 2 four times).
2. **Next, divide by the next smallest prime number (3):**
- \( 45 \div 3 = 15 \)
- \( 15 \div 3 = 5 \)
This gives us \( 3^2 \) (since we divided by 3 twice).
3. **Finally, what remains is 5, which is a prime number:**
- \( 5 \div 5 = 1 \)
So, we have \( 5^1 \).
Putting it all together:
\[ 720 = 2^4 \times 3^2 \times 5 \]
**Prime Factorization of 720:**
\[ 720 = 2^4 \times 3^2 \times 5 \]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To express 720 as a product of its prime factors, we start with the number 720 and divide it by the smallest prime number, which is 2. Continuously dividing by 2 until we can no longer do so gives us: 720 ÷ 2 = 360 360 ÷ 2 = 180 180 ÷ 2 = 90 90 ÷ 2 = 45 At this point, 45 can no longer be divided by 2, so we move to the next prime number, which is 3: 45 ÷ 3 = 15 15 ÷ 3 = 5 Finally, 5 is a prime number itself, and we cannot divide it further. Now we can compile our prime factors: 720 = 2^4 × 3^2 × 5^1. So, 720 can be written as the product of its prime factors: 2^4 × 3^2 × 5.
