What is the prime factorization of 385?
Understand the Problem
The question is asking for the prime factorization of the number 385, which means we need to express it as a product of its prime factors.
Answer
The prime factorization of 385 is $5 \times 7 \times 11$.
Answer for screen readers
The prime factorization of 385 is $5 \times 7 \times 11$.
Steps to Solve
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Start with the number 385 To begin, we need to find the prime factors of the number 385. We will start by checking for divisibility by the smallest prime number, which is 2.
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Check divisibility by 2 Since 385 is an odd number, it is not divisible by 2. Next, we move to the next prime number, which is 3.
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Check divisibility by 3 To check if 385 is divisible by 3, we can add the digits of 385: $3 + 8 + 5 = 16$. Since 16 is not divisible by 3, we conclude that 385 is also not divisible by 3. The next prime number to check is 5.
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Check divisibility by 5 Since 385 ends in a 5, it is divisible by 5. We will divide 385 by 5: $$ 385 \div 5 = 77 $$
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Factor 77 into primes Now we need to find the prime factors of 77. We start again with the smallest prime number, 2.
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Check divisibility by 2 Again, since 77 is odd, it is not divisible by 2. We check the next prime, which is 3.
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Check divisibility by 3 Adding the digits of 77 gives $7 + 7 = 14$, which is not divisible by 3. Now we check divisibility by 5.
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Check divisibility by 5 77 does not end in a 5 or 0, so it is not divisible by 5. We will check the next prime number, which is 7.
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Check divisibility by 7 Now, we divide 77 by 7: $$ 77 \div 7 = 11 $$ Since 11 is a prime number, we stop here.
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Compile the prime factorization Now we can express 385 as a product of its prime factors: $$ 385 = 5 \times 7 \times 11 $$
The prime factorization of 385 is $5 \times 7 \times 11$.
More Information
The prime factorization shows the building blocks of the number 385, which can be useful in various mathematical applications, such as finding the greatest common divisor (GCD) or the least common multiple (LCM).
Tips
- A common mistake is assuming a number is prime without checking for divisibility by smaller prime numbers. Always verify by dividing by all prime numbers up to the square root of the number.
