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:
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Divide by 2 (the smallest prime): \[ 560 \div 2 = 280 \]
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Continue dividing by 2: \[ 280 \div 2 = 140 \] \[ 140 \div 2 = 70 \] \[ 70 \div 2 = 35 \]
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Now divide by the next smallest prime (3):
- 35 is not divisible by 3.
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Divide by 5 (the next smallest prime): \[ 35 \div 5 = 7 \]
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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 \(2^4 \times 5^1 \times 7^1\).