Question
What are the prime factors of 700?
Question 8 options:
A)
350 × 2
B)
2 × 2 × 2 × 5 × 5 × 7
C)
2 × 2 × 25 × 7
D)
2 × 2 × 5 × 5 × 7
Question 8 options:
A)
350 × 2
B)
2 × 2 × 2 × 5 × 5 × 7
C)
2 × 2 × 25 × 7
D)
2 × 2 × 5 × 5 × 7
Answers
GPT-4o mini
To find the prime factors of 700, we can start by dividing it by the smallest prime number, which is 2, and proceed with subsequent divisions.
1. **Divide by 2:**
- \( 700 \div 2 = 350 \)
2. **Divide by 2 again:**
- \( 350 \div 2 = 175 \)
3. **Now divide by 5 (the next smallest prime factor):**
- \( 175 \div 5 = 35 \)
4. **Divide by 5 again:**
- \( 35 \div 5 = 7 \)
5. **7 is a prime number and cannot be divided further.**
Assembling all the prime factors, we have:
- \( 700 = 2 \times 2 \times 5 \times 5 \times 7 \)
- This can also be written as \( 2^2 \times 5^2 \times 7 \).
Now, comparing with the provided options, we find:
- D) \( 2 \times 2 \times 5 \times 5 \times 7 \) matches our factorization.
Thus, the correct answer is **D) 2 × 2 × 5 × 5 × 7**.
1. **Divide by 2:**
- \( 700 \div 2 = 350 \)
2. **Divide by 2 again:**
- \( 350 \div 2 = 175 \)
3. **Now divide by 5 (the next smallest prime factor):**
- \( 175 \div 5 = 35 \)
4. **Divide by 5 again:**
- \( 35 \div 5 = 7 \)
5. **7 is a prime number and cannot be divided further.**
Assembling all the prime factors, we have:
- \( 700 = 2 \times 2 \times 5 \times 5 \times 7 \)
- This can also be written as \( 2^2 \times 5^2 \times 7 \).
Now, comparing with the provided options, we find:
- D) \( 2 \times 2 \times 5 \times 5 \times 7 \) matches our factorization.
Thus, the correct answer is **D) 2 × 2 × 5 × 5 × 7**.