What is the sum of the prime factors of $91$?

To find the sum of the prime factors of $ 91 $, we first need to determine its prime factors.

1. Start by dividing $ 91 $ by the smallest prime number, which is $ 2 $. Since $ 91 $ is odd, it is not divisible by $ 2 $.

2. Next, check divisibility by $ 3 $. The sum of the digits of $ 91 $ is $ 9 + 1 = 10 $, which is not divisible by $ 3 $, so $ 91 $ is not divisible by $ 3 $.

3. Then, check divisibility by $ 5 $. Numbers divisible by $ 5 $ end in $ 0 $ or $ 5 $, and $ 91 $ does not, so it is not divisible by $ 5 $.

4. Now check divisibility by $ 7 $. Dividing $ 91 $ by $ 7 $ gives:

   \[
   91 \div 7 = 13
   \]

   So, $ 91 = 7 \times 13 $.

Both $ 7 $ and $ 13 $ are prime numbers. Therefore, the prime factors of $ 91 $ are $ 7 $ and $ 13 $.

The sum of the prime factors is:

\[
7 + 13 = 20
\]

So, the sum of the prime factors of $ 91 $ is $ \boxed{20} $.

Would you like more details or have any questions?

Here are 5 related questions:

1. What are the prime factors of $ 182 $?
2. How do you determine if a number is prime?
3. What is the greatest common divisor (GCD) of $ 91 $ and $ 182 $?
4. How can you find the prime factorization of a number?
5. What is the least common multiple (LCM) of $ 91 $ and $ 13 $?

**Tip:** When checking for divisibility by primes, you only need to test divisibility up to the square root of the number.

Discover how to find the sum of the prime factors of 91 with a step-by-step explanation. Learn about prime numbers, factorization, and their applications. Suitable for Grades 7-9 students and anyone interested in number theory.

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