Factorization Breakdown: Listing All Factors of 99

Q: What's the difference between factors and prime factors?

Factors are all numbers that divide evenly into 99 (like 1, 3, 9, 11, 33, 99). Prime factors are only the prime numbers that multiply together to make 99 (3, 3, 11).

Q: Why do I write 3 twice in the answer?

Because 3 appears twice in the prime factorization! Since $ 99 = 3^2 \times 11 $, we need both 3's to rebuild the original number.

Q: How do I know when to stop dividing?

Stop when you reach a prime number. Since 11 cannot be divided by any smaller primes (2, 3, 5, 7), it's prime and we're done!

Q: Can I start with a different prime number?

Always start with the smallest prime (2, then 3, then 5...). This ensures you find the complete factorization systematically without missing any factors.

Prime Factorization with Repeated Division

Write all the factors of the following number: $99$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find all the prime factors of the number

00:04 Split the digits and multiply them together

00:07 Divide this product by a prime factor

00:13 Possible, therefore this factor is a factor of the number

00:16 Divide by 3, and continue with the result to find the factors

00:23 The ones digit is 3, therefore 3 is definitely a prime factor

00:27 Divide by 3, and continue with the result to find the factors

00:31 And the result is a prime number, therefore it's a factor by itself

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write all the factors of the following number: $99$

Step-by-step solution

To solve this problem of finding the factors of $99$ , we will apply the process of prime factorization step-by-step:

Step 1: Begin with the smallest prime number, which is $2$ . Since $99$ is odd, it is not divisible by $2$ . Therefore, we proceed to the next prime number, $3$ .

Step 2: Check divisibility by $3$ . The sum of the digits of $99$ is $9 + 9 = 18$ , which is divisible by $3$ , indicating that $99$ is divisible by $3$ . Performing the division, we have:

99 \div 3 = 33

Step 3: We have $33$ now. Check for divisibility by $3$ again, as $33 \div 3 = 11$ . Now, $11$ is left, which is a prime number. Therefore, we have our factors.

The prime factorization of $99$ is:

99 = 3 \times 3 \times 11

These numbers are the prime factors of $99$ . Thus, the correct choice from the options provided is:

$11, 3, 3$ .

Final Answer

$11,3,3$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide by smallest prime until only primes remain
Technique: Check divisibility by 3: sum of digits $9+9=18$ is divisible by 3
Check: Multiply prime factors back: $3 \times 3 \times 11 = 99$ ✓

Common Mistakes

Avoid these frequent errors

Confusing prime factorization with listing all factors
Don't list all possible divisors like 1, 3, 9, 11, 33, 99 = wrong type of factors! The question asks for prime factors only. Always find prime numbers that multiply to give the original number.

Practice Quiz

Test your knowledge with interactive questions

Write all the factors of the following number: $$ 6 $$

FAQ

Everything you need to know about this question

What's the difference between factors and prime factors?

Factors are all numbers that divide evenly into 99 (like 1, 3, 9, 11, 33, 99). Prime factors are only the prime numbers that multiply together to make 99 (3, 3, 11).

Why do I write 3 twice in the answer?

Because 3 appears twice in the prime factorization! Since $99 = 3^2 \times 11$ , we need both 3's to rebuild the original number.

How do I know when to stop dividing?

Stop when you reach a prime number. Since 11 cannot be divided by any smaller primes (2, 3, 5, 7), it's prime and we're done!

What if I can't remember if a number is prime?

Test divisibility by small primes: 2, 3, 5, 7, 11... If none divide evenly and you've tested up to the square root, it's prime. For 11, test 2 and 3 - neither works, so 11 is prime!

Can I start with a different prime number?

Always start with the smallest prime (2, then 3, then 5...). This ensures you find the complete factorization systematically without missing any factors.

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