Write 850 as the product of its prime factors.
Understand the Problem
The question is asking us to find the prime factorization of the number 850, which means expressing it as a product of its prime numbers.
Answer
The prime factorization of 850 is $2 \times 5^2 \times 17$.
Answer for screen readers
The prime factorization of 850 is $2 \times 5^2 \times 17$.
Steps to Solve
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Divide by the smallest prime number Start by dividing 850 by the smallest prime number, which is 2. $$ 850 ÷ 2 = 425 $$
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Continue with the next smallest prime Next, check if 425 can be divided by the next smallest prime, which is 3. Since 425 is not divisible by 3, we try the next prime, which is 5. $$ 425 ÷ 5 = 85 $$
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Keep factoring Now, we need to factor 85. We check for divisibility by the smallest primes starting with 5, since 85 ends in 5. $$ 85 ÷ 5 = 17 $$
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Identify the last prime The number 17 is itself a prime number, so we stop here.
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Write the prime factorization Now we can express 850 as the product of its prime factors. $$ 850 = 2 × 5^2 × 17 $$
The prime factorization of 850 is $2 \times 5^2 \times 17$.
More Information
The prime factorization process identifies prime numbers that can multiply together to give the original number. In this case, we've found 2, 5, and 17 as the primes that multiply to form 850.
Tips
A common mistake is to forget to check if a number is prime before concluding the factorization. Make sure to stop dividing when you reach a prime number.
