Prime factorization of 2000
Understand the Problem
The question is asking for the prime factorization of the number 2000, which involves breaking it down into its prime factors.
Answer
The prime factorization of 2000 is $2^4 \cdot 5^3$.
Answer for screen readers
The prime factorization of 2000 is $2^4 \cdot 5^3$.
Steps to Solve
- Start with the number 2000
We begin by dividing 2000 by the smallest prime number, which is 2.
$$ 2000 \div 2 = 1000 $$
- Continue dividing by 2
We can still divide 1000 by 2, as it is even.
$$ 1000 \div 2 = 500 $$
- Divide by 2 again
Next, we divide 500 by 2.
$$ 500 \div 2 = 250 $$
- Keep dividing by 2
We keep dividing 250 by 2.
$$ 250 \div 2 = 125 $$
- Switch to the next prime number
Now, 125 is not divisible by 2. We change to the next prime number, which is 5.
$$ 125 \div 5 = 25 $$
- Divide by 5 again
We continue dividing 25 by 5.
$$ 25 \div 5 = 5 $$
- Final division by 5
Finally, we divide 5 by 5.
$$ 5 \div 5 = 1 $$
- Write the prime factorization
When we have completed all divisions, we can express the prime factorization of 2000 in terms of the prime factors used.
The prime factorization is: $2^4 \cdot 5^3$
The prime factorization of 2000 is $2^4 \cdot 5^3$.
More Information
Prime factorization is useful in many areas of mathematics, including simplifying fractions and finding the greatest common divisors. The number 2000 can be shown as the product of its prime factors, highlighting how numbers can be broken down into their building blocks.
Tips
- Forgetting to check divisibility by smaller primes: Always start with the smallest primes and verify if the number can still be divided.
- Miscounting the number of times a prime factor divides into the number: Keep careful track of how many times you've divided each prime factor.
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