What is the prime factorization of 525?
Understand the Problem
The question is asking for the prime factorization of the number 525, which involves determining which prime numbers multiply together to produce this number. To solve this, we will divide 525 by the smallest prime numbers until we reach the final factors.
Answer
$$525 = 3 \times 5^2 \times 7$$
Answer for screen readers
The prime factorization of 525 is given by:
$$525 = 3 \times 5^2 \times 7$$
Steps to Solve
- Start with the smallest prime number
We begin by dividing 525 by the smallest prime number, which is 2. However, since 525 is an odd number, it's not divisible by 2.
- Check divisibility by the next prime number
Next, we check if 525 is divisible by 3:
$$525 \div 3 = 175$$
Since there is no remainder, we can proceed with 3 as one of the factors.
- Continue with the next quotient
Now we take the quotient 175 and check if it's divisible by 3 again:
$$175 \div 3 \approx 58.33$$
Since 175 is not divisible by 3, we move to the next prime number, which is 5.
- Divide by 5
We divide 175 by 5:
$$175 \div 5 = 35$$
This means 5 is another factor.
- Proceed with the next quotient
Now we take 35 and check if it's divisible by 5:
$$35 \div 5 = 7$$
This tells us that 5 is a factor again.
- Check if the last quotient is prime
We are left with 7, which is a prime number itself.
- Combine all the factors for prime factorization
Now we can compile all the factors found so far:
$$525 = 3 \times 5^2 \times 7$$
The prime factorization of 525 is given by:
$$525 = 3 \times 5^2 \times 7$$
More Information
Prime factorization is a way to express numbers as products of their prime factors. Understanding how to break down a number into primes is fundamental in number theory and has applications in areas such as cryptography.
Tips
- A common mistake is forgetting to check divisibility for all prime numbers in ascending order. Always check for the smallest primes first.
- Another mistake is miscalculating the divisions or forgetting to note when a number is no longer divisible by a certain prime.
