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): $$560÷2=280$$

2. Continue dividing by 2: $$280÷2=140$$ $$140÷2=70$$ $$70÷2=35$$

3. Now divide by the next smallest prime (3):

   • 35 is not divisible by 3.

4. Divide by 5 (the next smallest prime): $$35÷5=7$$

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 $2^4\times 5^1\times 7^1$.