What are the prime factors of 385?
Understand the Problem
The question is asking for the prime factors of the number 385. This means we need to find which prime numbers multiply together to give us 385.
Answer
The prime factors of 385 are $5$, $7$, and $11$.
Answer for screen readers
The prime factors of 385 are $5$, $7$, and $11$.
Steps to Solve
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Start with the number
We begin with the number 385 and identify the smallest prime number to test for divisibility. -
Check divisibility by 2
Since 385 is odd, it is not divisible by 2. We move on to the next prime. -
Check divisibility by 3
To check if 385 is divisible by 3, we sum the digits: $3 + 8 + 5 = 16$. Since 16 is not divisible by 3, 385 is also not divisible by 3. -
Check divisibility by 5
The last digit of 385 is 5, so it is divisible by 5. We can perform the division:
$$ 385 \div 5 = 77 $$
Now we have 5 as one of our prime factors. -
Factor 77 further
Next, we need to factor 77. We again check the smallest primes. 77 is not even, so we skip 2, and the sum of its digits ($7 + 7 = 14$) means it isn't divisible by 3 either. -
Check divisibility by 7
Next, we test 7:
$$ 77 \div 7 = 11 $$
So, we add 7 as another prime factor, and now we have 5, 7, and 11. -
Final prime check
The number 11 is a prime number, so we've completely factored 385. -
List the prime factors
The prime factors of 385 are: 5, 7, 11.
The prime factors of 385 are $5$, $7$, and $11$.
More Information
Prime factorization is useful in many areas of mathematics. For example, understanding the prime factors helps in simplifying fractions, finding least common multiples, and solving problems in number theory.
Tips
- Forgetting to check primes in ascending order can lead you to miss factors.
- Miscalculating when dividing can result in incorrect factors; always double-check divisions.
