Question

what numbers i can use to make in exponents a prime factorization of 560 multipication

Answer 1

To find the prime factorization of 560, we can start by dividing it by the smallest prime numbers. Here’s how you can do it step-by-step:

1. **Divide by 2 (the smallest prime)**:
\[
560 \div 2 = 280
\]

2. **Continue dividing by 2**:
\[
280 \div 2 = 140
\]
\[
140 \div 2 = 70
\]
\[
70 \div 2 = 35
\]

3. **Now divide by the next smallest prime (3)**:
- 35 is not divisible by 3.

4. **Divide by 5 (the next smallest prime)**:
\[
35 \div 5 = 7
\]

5. **Finally, 7 is a prime number**.

So, putting it all together, we took:

- \(2^4\) (because we divided by 2 four times)
- \(5^1\) (because we divided by 5 once)
- \(7^1\) (because we have one 7)

Thus, the prime factorization of 560 can be written as:
\[
560 = 2^4 \times 5^1 \times 7^1
\]

To summarize, the prime factorization of 560 is \(2^4 \times 5^1 \times 7^1\).