What is the prime factorization of 10000?
Understand the Problem
The question is asking for the prime factorization of the number 10000, which involves expressing it as a product of its prime factors.
Answer
The prime factorization of 10000 is \( 2^4 \times 5^4 \).
Answer for screen readers
The prime factorization of 10000 is ( 2^4 \times 5^4 ).
Steps to Solve
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Start with the number
We begin with the number 10000. -
Identify the prime factor 2
Since 10000 is even, we can start dividing by 2:
$$ 10000 \div 2 = 5000 $$
We can keep dividing by 2:
$$ 5000 \div 2 = 2500 $$
$$ 2500 \div 2 = 1250 $$
$$ 1250 \div 2 = 625 $$
625 is not divisible by 2 anymore. -
Identify the next prime factor 5
Now we divide by 5:
$$ 625 \div 5 = 125 $$
$$ 125 \div 5 = 25 $$
$$ 25 \div 5 = 5 $$
$$ 5 \div 5 = 1 $$
Now we have reached 1. -
Summary of factors
We have divided 10000 as follows:
- Divided by 2 four times: $2^4$
- Divided by 5 four times: $5^4$
Thus, the prime factorization of 10000 is $2^4 \times 5^4$.
The prime factorization of 10000 is ( 2^4 \times 5^4 ).
More Information
The number 10000 can also be represented as ( 10^4 ) since ( 10 = 2 \times 5 ). This shows that understanding the relationship between bases and their prime factors can simplify calculations.
Tips
- Forgetting to continue dividing by prime factors until you reach 1. To avoid this, keep dividing until you can no longer divide evenly.
- Miscounting the number of times you divide by a prime factor. It helps to keep track of your calculations carefully.
