Question

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

Answer 1

To find the prime factorization of 560, we start by dividing it by the smallest prime numbers and continue dividing until we reach 1. Here's how you can do it:

1. **Divide by 2** (the smallest prime number):
- \( 560 \div 2 = 280 \)
- \( 280 \div 2 = 140 \)
- \( 140 \div 2 = 70 \)
- \( 70 \div 2 = 35 \)

2. **Now divide by 5** (the next smallest prime number):
- \( 35 \div 5 = 7 \)

3. **Finally, 7 is also a prime number**.

So, we have divided 560 down to the prime factors:

- We divided by \(2\) three times, giving us \(2^3\).
- We divided by \(5\) once, giving us \(5^1\).
- We divided by \(7\) once, giving us \(7^1\).

Putting it all together, the prime factorization of \(560\) is:

\[
560 = 2^3 \times 5^1 \times 7^1
\]