prime factor of 320
Understand the Problem
The question is asking for the prime factors of the number 320. To solve this, we will break down the number into its prime components by dividing it by the smallest prime numbers until we reach 1.
Answer
The prime factors of 320 are $2^6$ and $5^1$.
Answer for screen readers
The prime factors of 320 are $2^6$ and $5^1$.
Steps to Solve
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Start with the number 320 We begin with our target number: 320.
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Divide by the smallest prime (2) Since 320 is even, we divide it by 2. $$ 320 \div 2 = 160 $$
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Continue dividing by 2 We continue dividing by 2 since 160 is still even. $$ 160 \div 2 = 80 $$
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Repeat division by 2 Again, since 80 is even, we divide by 2. $$ 80 \div 2 = 40 $$
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Keep dividing by 2 We divide 40 by 2, as it is still even. $$ 40 \div 2 = 20 $$
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Divide by 2 again Next, we divide 20 by 2. $$ 20 \div 2 = 10 $$
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One more division by 2 We divide 10 by 2 once more. $$ 10 \div 2 = 5 $$
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Final division by the next prime (5) Now, we cannot divide 5 by 2 anymore. We switch to the next prime, which is 5. $$ 5 \div 5 = 1 $$
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List the prime factors From our divisions, we find that the prime factors of 320 are all the 2's and the 5: $$ 320 = 2^6 \times 5^1 $$
The prime factors of 320 are $2^6$ and $5^1$.
More Information
The prime factorization of a number involves breaking it down into the prime numbers that multiply together to yield the original number. Prime numbers are those greater than 1 that have no divisors other than 1 and themselves. Understanding prime factorization is fundamental for concepts in number theory and is very useful in simplifying fractions or finding the greatest common divisor.
Tips
- Forgetting to continue dividing even after reaching smaller numbers like 10. Remember to go further until you can’t divide evenly any longer.
- Confusing composite numbers with prime numbers. Always check if the number can be divided by smaller primes.
