Find All Factors of 12: A Comprehensive Guide

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

All factors of 12 are: 1, 2, 3, 4, 6, 12. But prime factors are only the prime numbers that multiply to make 12: just 2, 2, and 3!

Q: Why does the order of prime factors matter in the answer choices?

The mathematical value doesn't change, but test questions often list factors in a specific order. Look for the choice that matches your factorization: $ 2 \times 2 \times 3 $.

Q: Do I always start dividing by 2?

Always start with the smallest prime that divides your number. Since 2 is the smallest prime, try it first. If the number is odd, move to 3, then 5, etc.

Q: How do I know 3 is prime?

A prime number only has two factors: 1 and itself. Since 3 can only be divided evenly by 1 and 3, it's prime. Other small primes: 2, 5, 7, 11, 13.

Prime Factorization with Ordered Factor Lists

Write all the factors of the following number: $12$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find all the prime factors of this number. Ready?

00:08 Look, the last digit is 2. So, 2 is definitely a prime factor.

00:13 Divide the number by 2. Then, use the result to find more factors.

00:19 Now, the last digit is 6. Again, 2 is a prime factor.

00:23 Divide by 2 again. Keep going to find more factors.

00:27 Finally, our result is a prime number. This means it's a factor on its own.

00:33 And that's how you solve this problem! Great job!

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: $12$

Step-by-step solution

To find all the factors of 12, we will perform a prime factorization:

Start with the smallest prime number, 2. Since 12 is divisible by 2, we divide 12 by 2:

$12 \div 2 = 6$

Next, we have 6, which is also divisible by 2:

$6 \div 2 = 3$

Now we are left with 3, which is a prime number and divisible by itself:

$3 \div 3 = 1$

Since we reached 1, the division process stops.

Therefore, the prime factors of 12 are $2, 2,$ and $3$ .

Expressing 12 using these factors: $12 = 2 \times 2 \times 3$ .

Thus, the correct list of factors is given by choice 2: $3, 2, 2$ .

Final Answer

$3,2,2$

Key Points to Remember

Essential concepts to master this topic

Method: Divide repeatedly by smallest prime until reaching 1
Technique: Start with 2: 12 ÷ 2 = 6, then 6 ÷ 2 = 3
Check: Multiply factors together: 2 × 2 × 3 = 12 ✓

Common Mistakes

Avoid these frequent errors

Confusing prime factors with all factors
Don't list divisors like 1, 2, 3, 4, 6, 12 = wrong type of factors! The question asks for prime factorization, not all divisors. Always break the number into prime numbers only.

Practice Quiz

Test your knowledge with interactive questions

Write all the factors of the following number: $$ 5 $$

FAQ

Everything you need to know about this question

What's the difference between factors and prime factors?

All factors of 12 are: 1, 2, 3, 4, 6, 12. But prime factors are only the prime numbers that multiply to make 12: just 2, 2, and 3!

Why does the order of prime factors matter in the answer choices?

The mathematical value doesn't change, but test questions often list factors in a specific order. Look for the choice that matches your factorization: $2 \times 2 \times 3$ .

Do I always start dividing by 2?

Always start with the smallest prime that divides your number. Since 2 is the smallest prime, try it first. If the number is odd, move to 3, then 5, etc.

What if I can't divide by any more primes?

When you reach a prime number (like 3 in this problem), divide it by itself to get 1. Once you reach 1, you're done! List all the primes you used.

How do I know 3 is prime?

A prime number only has two factors: 1 and itself. Since 3 can only be divided evenly by 1 and 3, it's prime. Other small primes: 2, 5, 7, 11, 13.

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