What are the prime factors of 119?
Understand the Problem
The question is asking for the prime factors of the number 119, which requires finding the prime numbers that, when multiplied together, give the product of 119.
Answer
The prime factors of 119 are $7$ and $17$.
Answer for screen readers
The prime factors of 119 are $7$ and $17$.
Steps to Solve
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Start with the number 119
We need to find the prime factors of 119. Begin by testing small prime numbers to see if they divide evenly into 119. -
Testing for divisibility by 2
Since 119 is odd, it is not divisible by 2. Move to the next prime number. -
Testing for divisibility by 3
Add the digits of 119: $1 + 1 + 9 = 11$. Since 11 is not divisible by 3, 119 is not divisible by 3. Move to the next prime number. -
Testing for divisibility by 5
The last digit of 119 is 9, which is not 0 or 5. Therefore, 119 is not divisible by 5. Continue to the next prime number. -
Testing for divisibility by 7
Now check 7:
$$119 \div 7 = 17$$
This calculation shows that 119 is divisible by 7, resulting in 17. -
Factorization result
Since both 7 and 17 are prime numbers, the prime factorization of 119 is:
$$119 = 7 \times 17$$
The prime factors of 119 are $7$ and $17$.
More Information
The prime factorization can be useful in various mathematical applications, including simplifying fractions and finding greatest common divisors. It's also interesting to note that 119 is the product of two prime numbers, making it a semiprime.
Tips
- Skipping small prime numbers: Some might forget to test smaller primes such as 2, 3, and 5.
- Mistaking composite numbers for primes: Ensure that both factors (7 and 17) are identified as prime numbers to avoid errors.
