What is the prime factorisation of 2800?
Understand the Problem
The question is asking for the prime factorization of the number 2800, which means we need to find the prime numbers that multiply together to give 2800.
Answer
The prime factorization of 2800 is $2^4 \times 5^2 \times 7$.
Answer for screen readers
The prime factorization of 2800 is $2^4 \times 5^2 \times 7$.
Steps to Solve
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Start with the number We begin with the number 2800 that we need to factor.
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Divide by the smallest prime number The smallest prime number is 2. We check if 2800 is divisible by 2: $$ 2800 \div 2 = 1400 $$ So we can write: $$ 2800 = 2 \times 1400 $$
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Repeat the division with 2 We can continue factoring 1400 by 2: $$ 1400 \div 2 = 700 $$ Now we have: $$ 2800 = 2 \times 2 \times 700 $$
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Continue factoring by 2 Next, we factor 700 by 2 again: $$ 700 \div 2 = 350 $$ Now it looks like: $$ 2800 = 2 \times 2 \times 2 \times 350 $$
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Continue with the next step Next, we factor 350 by 2: $$ 350 \div 2 = 175 $$ So we write: $$ 2800 = 2 \times 2 \times 2 \times 2 \times 175 $$
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Factor 175 by the next smallest prime (5) Now, we switch to the next smallest prime, which is 5: $$ 175 \div 5 = 35 $$ Now we have: $$ 2800 = 2 \times 2 \times 2 \times 2 \times 5 \times 35 $$
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Factor 35 by the next smallest prime (5) again Now we can factor 35 by 5 again: $$ 35 \div 5 = 7 $$ This results in: $$ 2800 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 7 $$
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Complete the prime factorization Now we can summarize the complete prime factorization: $$ 2800 = 2^4 \times 5^2 \times 7 $$
The prime factorization of 2800 is $2^4 \times 5^2 \times 7$.
More Information
Prime factorization breaks down a number into its smallest prime components. In this case, 2800 multiplies together the primes $2$, $5$, and $7$. This method of factorization is essential in number theory and helps in various mathematical applications.
Tips
- Forgetting to check for all prime factors: It's tempting to stop once you reach a couple of factors. Ensure to factor until you can no longer divide by prime numbers.
- Not using primes: Students may mistakenly use composite numbers instead of primes in their factorizations.
