What are the prime factors of 525?
Understand the Problem
The question is asking us to identify the prime factors of the number 525. To solve this, we will perform prime factorization by dividing 525 by the smallest prime numbers until we cannot divide any longer.
Answer
The prime factorization of 525 is $3 \times 5^2 \times 7$.
Answer for screen readers
The prime factorization of 525 is given by: $$ 525 = 3 \times 5^2 \times 7 $$
Steps to Solve
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Start with the Number We begin with the number 525.
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Divide by the Smallest Prime The smallest prime number is 2. Check if 525 is divisible by 2. Since 525 is odd, it is not divisible by 2. We move to the next prime number, which is 3.
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Check Divisibility by 3 To check if 525 is divisible by 3, we can sum its digits: $5 + 2 + 5 = 12$. Since 12 is divisible by 3, we divide 525 by 3: $$ 525 \div 3 = 175 $$
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Continue with New Quotient Now we have 175. Checking divisibility by 3 again, we sum the digits of 175: $1 + 7 + 5 = 13$, which is not divisible by 3. We move to the next prime, 5.
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Divide by 5 Since the last digit of 175 is 5, it is divisible by 5. Now, we divide: $$ 175 \div 5 = 35 $$
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Factor 35 Next, we factor 35. Since 35 ends with 5, we divide by 5 again: $$ 35 \div 5 = 7 $$
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Finish with the Last Number Finally, we have reached 7, which is a prime number itself. So, we cannot factor it any further.
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List Prime Factors The prime factors of 525 are collected: $3$, $5$, $5$, and $7$.
The prime factorization of 525 is given by: $$ 525 = 3 \times 5^2 \times 7 $$
More Information
The prime factors of a number are the prime numbers that multiply together to give that number. Prime factorization is a crucial concept in number theory and has applications in various areas such as cryptography and computer science.
Tips
- Confusing prime factors with composite factors. Ensure that only prime numbers are used in the factorization.
- Forgetting to check if a factor is prime before concluding the factorization. Always verify primality.
