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

1 answer

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 \(2^4 \times 5^1 \times 7^1\).