What is the prime factorization of 2800?
Understand the Problem
The question is asking for the prime factorization of the number 2800, which means we need to break it down into its prime factors.
Answer
The prime factorization of 2800 is $2^3 \times 5^2 \times 7$.
Answer for screen readers
The prime factorization of 2800 is $2^3 \times 5^2 \times 7$.
Steps to Solve
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Start with the Number We begin with the number 2800.
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Divide by 10 Since 2800 ends in a zero, we can factor out 10: $$ 2800 \div 10 = 280 $$ Now, we have: $$ 2800 = 10 \times 280 $$
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Factor 10 Next, we factor 10 into primes: $$ 10 = 2 \times 5 $$ Now we have: $$ 2800 = (2 \times 5) \times 280 $$
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Factor 280 Now let's focus on 280. Since it also ends in zero, we can factor out 10 again: $$ 280 \div 10 = 28 $$ So, we can write: $$ 280 = (2 \times 5) \times 28 $$ Therefore, $$ 2800 = (2 \times 5) \times (2 \times 5) \times 28 $$
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Continue with 28 Now we factor 28: $$ 28 = 2 \times 14 $$ So we write: $$ 2800 = (2 \times 5)^2 \times (2 \times 14) $$
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Factor 14 Finally, we factor 14: $$ 14 = 2 \times 7 $$
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Combine All the Factors Putting all this together, we multiply the factors: $$ 2800 = 2^3 \times 5^2 \times 7 $$
The prime factorization of 2800 is $2^3 \times 5^2 \times 7$.
More Information
The prime factorization is useful in many areas of mathematics, including simplifying fractions and finding the greatest common divisors. The number 2800 can also be constructed as the product of the smallest prime numbers raised to their respective powers.
Tips
- Not recognizing factors: Sometimes, it's easy to overlook zeros and forget to factor them out. Always check for factors of 10 first for numbers ending in zero.
- Skipping steps: Ensure you break down each factor until you reach only primes.
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