What is the prime factorization of 350?
Understand the Problem
The question is asking for the prime factorization of the number 350, which means we need to express 350 as a product of its prime factors.
Answer
2 \times 5^2 \times 7
Answer for screen readers
The prime factorization of 350 is 2 \times 5^2 \times 7
Steps to Solve
- Divide by the smallest prime number
First, divide 350 by the smallest prime number, which is 2.
$$ 350 \div 2 = 175 $$
So, 2 is one of the prime factors, and we continue with the quotient 175.
- Continue dividing by the next smallest prime number
Next, we take 175 and divide it by the smallest prime number that is a factor. Since 175 is odd, the next prime is 5.
$$ 175 \div 5 = 35 $$
So, 5 is another prime factor, and we continue with the quotient 35.
- Repeat the process
Now, we take 35 and again divide by 5.
$$ 35 \div 5 = 7 $$
This leaves us with the prime number 7. We stop here because 7 is a prime number.
- Write out the prime factors
Combine all the prime factors we have found.
$$ 350 = 2 \times 5^2 \times 7 $$
The prime factorization of 350 is 2 \times 5^2 \times 7
More Information
Prime factors are the building blocks of a number. They are useful in various areas of mathematics including number theory and cryptography.
Tips
A common mistake when finding prime factors is not dividing by the smallest prime number first. Always start with the smallest prime and move upwards.
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