What are the prime factors of 95?
Understand the Problem
The question is asking for the prime factors of the number 95. To solve this, we need to identify the prime numbers that multiply together to give the product of 95.
Answer
The prime factors of 95 are $5$ and $19$.
Answer for screen readers
The prime factors of 95 are 5 and 19.
Steps to Solve
- Determine the smallest prime number for division
Start with the smallest prime number, which is 2. Since 95 is odd, it cannot be divided by 2.
- Check the next prime number
Next, check 3. Adding the digits of 95 gives $9 + 5 = 14$, which is not divisible by 3. Therefore, 95 is not divisible by 3.
- Check the next prime number
Now, check 5. Since 95 ends with a 5, it is divisible by 5.
Perform the division:
$$ 95 \div 5 = 19 $$
- Check if the quotient is prime
Now check if 19 is a prime number. A prime number is greater than 1 and has no divisors other than 1 and itself. The only divisors of 19 are 1 and 19, so 19 is prime.
- List the prime factors
The prime factorization of 95 is therefore $5 \times 19$.
The prime factors of 95 are 5 and 19.
More Information
The number 95 can only be expressed as a product of the prime numbers 5 and 19. Any other combinations would either involve non-prime factors or result in numbers other than 95.
Tips
- Confusing even numbers with prime numbers: Remember that 2 is the only even prime number; other even numbers are not prime.
- Not checking all the possible prime factors: It's important to continue checking larger prime numbers until the quotient is confirmed to be prime or factors are found.