What are the prime factors of 17?
Understand the Problem
The question is asking for the prime factors of the number 17. To solve this, we need to determine if 17 can be divided by any prime numbers without leaving a remainder.
Answer
The prime factors of 17 are $17$.
Answer for screen readers
The prime factors of 17 are 17 itself, as it is a prime number.
Steps to Solve
- Identify Prime Numbers Less Than 17
First, we need to list the prime numbers that are less than 17. The prime numbers are: 2, 3, 5, 7, 11, 13.
- Test Each Prime Number for Divisibility
Next, we will check if 17 can be divided by any of the listed prime numbers without leaving a remainder.
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First, check 2: $$ 17 \div 2 = 8.5 \quad (\text{not divisible}) $$
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Next, check 3: $$ 17 \div 3 \approx 5.67 \quad (\text{not divisible}) $$
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Check 5: $$ 17 \div 5 = 3.4 \quad (\text{not divisible}) $$
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Check 7: $$ 17 \div 7 \approx 2.43 \quad (\text{not divisible}) $$
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Check 11: $$ 17 \div 11 \approx 1.55 \quad (\text{not divisible}) $$
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Check 13: $$ 17 \div 13 \approx 1.31 \quad (\text{not divisible}) $$
- Conclude the Check
Since 17 is not divisible by any of the prime numbers less than itself, we conclude that 17 is a prime number.
The prime factors of 17 are 17 itself, as it is a prime number.
More Information
17 is one of the smallest prime numbers and is known as a prime number because it has no divisors other than 1 and itself. It’s often used in number theory and mathematics.
Tips
- Confusing prime numbers with composite numbers. Always remember that a prime number has only two distinct positive divisors: 1 and itself.
- Forgetting to test all prime numbers below the number in question.
