What is the prime factorization of 320?
Understand the Problem
The question is asking for the prime factors of the number 320. This means we need to break down 320 into the prime numbers that multiply together to yield 320.
Answer
$2^5 \times 5$
Answer for screen readers
The prime factorization of 320 is $2^5 \times 5$.
Steps to Solve
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Start with the number 320
We will begin by dividing 320 by the smallest prime number, which is 2.
$$ 320 \div 2 = 160 $$
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Continue dividing by 2
Since 160 is still an even number, we can divide it by 2 again.
$$ 160 \div 2 = 80 $$
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Keep dividing by 2
Next, we divide 80 by 2 again, as it is even.
$$ 80 \div 2 = 40 $$
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Continue with 2
We can divide 40 by 2 once more.
$$ 40 \div 2 = 20 $$
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Divide 20 by 2
We keep dividing 20 by 2, since it is even.
$$ 20 \div 2 = 10 $$
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Final division by 2
Finally, we divide 10 by 2 to get the last result.
$$ 10 \div 2 = 5 $$
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Identify the remaining number
Now, we have reached 5, which is also a prime number. -
List the prime factors
The prime factors we found are:
$$ 2, 2, 2, 2, 2, 5 $$
This can be expressed as:
$$ 2^5 \times 5 $$
The prime factorization of 320 is $2^5 \times 5$.
More Information
The prime factorization provides valuable insight into the properties of the number. Factors can help with understanding numbers in relation to their multiples and divisibility. The process of finding prime factors is a key skill in many areas of mathematics, including number theory.
Tips
- Skipping even numbers: Some may neglect further divisions with 2 until they reach an odd number or forget to continue dividing until they can't anymore.
- Miscounting prime factors: It's important to keep track of how many times each prime factor is used in the multiplication.
