Determine All Factors of the Number 18

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

All factors of 18 are: 1, 2, 3, 6, 9, 18. Prime factors are only the prime numbers that multiply together: 2, 3, 3. Prime factorization breaks down a number into its building blocks!

Q: Can a prime factor appear more than once?

Absolutely! In $ 18 = 2 \times 3 \times 3 $, the prime factor 3 appears twice. We write all instances: 2, 3, 3 (not just 2, 3).

Q: How do I know when I'm done factoring?

You're done when the final result is 1. For 18: $ 18 \div 2 = 9 $, $ 9 \div 3 = 3 $, $ 3 \div 3 = 1 $. When you reach 1, stop!

Q: What if I can't divide by 2?

If a number is odd, skip 2 and try the next prime: 3. For example, with 15, start with $ 15 \div 3 = 5 $, then $ 5 \div 5 = 1 $.

Prime Factorization with Repeated Factors

Write all the factors of the following number: $18$

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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

00:05 The ones digit is 8, therefore 2 is definitely a prime factor

00:09 Divide by 2, and continue with the result to find the factors

00:13 The ones digit is 9, therefore 3 is definitely a prime factor

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

00:20 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: $18$

Step-by-step solution

To solve this problem, we'll use prime factorization:

Step 1: Begin by dividing 18 by 2, the smallest prime number. $18 \div 2 = 9$ . Therefore, 2 is a factor.
Step 2: Now factor 9, which is the result from the previous division. The smallest prime factor of 9 is 3, since $9 \div 3 = 3$ . Thus, 3 is a factor.
Step 3: Continue with the result from step 2. Divide 3 by 3 (since $3 \div 3 = 1$ ). Another 3 is a factor.
Step 4: The final division of 1 means we have completely factorized the number.

In conclusion, the prime factors of 18 are $2, 3, 3$ . Our factorization shows that the correct answer choice corresponds to: $2, 3, 3$ .

Final Answer

$2,3,3$

Key Points to Remember

Essential concepts to master this topic

Definition: Prime factors are the prime numbers that multiply together
Method: Divide by smallest prime first: $18 \div 2 = 9$ , then $9 \div 3 = 3$
Check: Multiply all factors together: $2 \times 3 \times 3 = 18$ ✓

Common Mistakes

Avoid these frequent errors

Confusing prime factors with all factors
Don't list all factors like 1, 2, 3, 6, 9, 18 when asked for prime factorization! This gives the complete factor list instead of prime factors only. Always break down into 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?

All factors of 18 are: 1, 2, 3, 6, 9, 18. Prime factors are only the prime numbers that multiply together: 2, 3, 3. Prime factorization breaks down a number into its building blocks!

Why do we start with the smallest prime number?

Starting with 2 (the smallest prime) makes the process systematic and organized. You won't miss any factors, and it's easier to follow. Always go in order: 2, 3, 5, 7, 11...

Can a prime factor appear more than once?

Absolutely! In $18 = 2 \times 3 \times 3$ , the prime factor 3 appears twice. We write all instances: 2, 3, 3 (not just 2, 3).

How do I know when I'm done factoring?

You're done when the final result is 1. For 18: $18 \div 2 = 9$ , $9 \div 3 = 3$ , $3 \div 3 = 1$ . When you reach 1, stop!

What if I can't divide by 2?

If a number is odd, skip 2 and try the next prime: 3. For example, with 15, start with $15 \div 3 = 5$ , then $5 \div 5 = 1$ .

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