What is the prime factorization of 250?
Understand the Problem
The question is asking for the prime factorization of the number 250, meaning we need to express it as a product of its prime factors.
Answer
$2^1 imes 5^3$
Answer for screen readers
The prime factorization of 250 is $2^1 imes 5^3$
Steps to Solve
- Identify the smallest prime factor
We start with the smallest prime number, 2. Check if it divides 250.
$$\frac{250}{2} = 125$$
So, 250 can be written as $2 imes 125$.
- Find the prime factors of the remaining product
Next, we need to factorize 125. The smallest prime number that divides 125 is 5.
$$\frac{125}{5} = 25$$
So, 125 can be written as $5 imes 25$.
- Continue factoring until all factors are prime
Now, factorize 25. Again, the smallest prime number that divides 25 is 5.
$$\frac{25}{5} = 5$$
And, 25 can be written as $5 imes 5$.
- Combine all prime factors
Now, combine all the prime factors we found:
$$250 = 2 imes 5 imes 5 imes 5$$
In exponential form, this is:
$$250 = 2^1 imes 5^3$$
The prime factorization of 250 is $2^1 imes 5^3$
More Information
The prime factorization shows the product of prime numbers that multiply to 250. The sum of the exponents in the prime factorization of a number can reveal the count of its divisors.
Tips
A common mistake is to forget to factor fully, stopping at composite numbers. Ensure every factor is a prime number.
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