Identify All Divisors: Listing the Factors of 202

Q: How do I know when I've found all the factors?

Once you have the prime factorization, you can systematically create all factors. For $ 202 = 2 × 101 $, the factors are: 1, 2, 101, and 202. That's all of them!

Q: What if I can't tell if a number like 101 is prime?

Test divisibility by prime numbers up to the square root. Since $ \sqrt{101} ≈ 10 $, test 2, 3, 5, 7. If none divide evenly, it's prime!

Q: Why don't any of the answer choices show all four factors?

This appears to be an error in the question setup. The complete answer should be 1, 2, 101, 202. Always list all factors, not just some of them.

Q: Can I use a factor tree instead?

Absolutely! A factor tree is another great way to find prime factors. Start with 202, split it into $ 2 × 101 $, then confirm both 2 and 101 are prime.

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

Prime factors are the building blocks (2 and 101 for 202). All factors include every number that divides evenly: 1, 2, 101, and 202.

Prime Factorization with Composite Numbers

Write all the factors of the following number: $202$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find all prime factors of the number

00:03 The ones digit is 2, therefore 2 is definitely a prime factor

00:07 Divide by 2, and continue with the result to find the factors

00:10 And the result is a prime number, therefore it's a factor by itself

00:14 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: $202$

Step-by-step solution

To solve this problem, we need to determine all factors of the number 202.

Step 1: Prime Factorization of 202
To find the prime factors of 202, we begin by dividing by the smallest prime number:

$202 \div 2 = 101$

Step 2: Check if 101 is prime
101 cannot be divided evenly by any prime numbers up to its square root other than 1 and 101 itself. Therefore, 101 is a prime number.

Therefore, the prime factorization of 202 is $2 \times 101$ .

Step 3: Listing factors
The factors of a number are all possible products of its prime factors, including 1 and the number itself.

Starting with 1 (trivial factor) and ending with the number 202:
Single prime 2 gives us two factors: $1$ and $2$ .
The factor 101 (as $101 \times 1$ ) is next.
Combine $2$ and $101$ to get the factor $202$ .

Therefore, the factors of 202 are: $1, 2, 101,$ and $202$ .

In conclusion, after comparing with the provided choices, none of the exact choices given fully match as the factors of 202.

Final Answer

$101,2$

Key Points to Remember

Essential concepts to master this topic

Rule: All factors come from combinations of prime factors
Technique: Start with $202 ÷ 2 = 101$ , then verify 101 is prime
Check: Multiply all factor pairs: $1 × 202 = 202$ , $2 × 101 = 202$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include 1 and the number itself as factors
Don't skip 1 and 202 when listing factors = incomplete answer! Every number is always divisible by 1 and itself, so these are always factors. Always include 1 and the original number in your factor list.

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

How do I know when I've found all the factors?

Once you have the prime factorization, you can systematically create all factors. For $202 = 2 × 101$ , the factors are: 1, 2, 101, and 202. That's all of them!

What if I can't tell if a number like 101 is prime?

Test divisibility by prime numbers up to the square root. Since $\sqrt{101} ≈ 10$ , test 2, 3, 5, 7. If none divide evenly, it's prime!

Why don't any of the answer choices show all four factors?

This appears to be an error in the question setup. The complete answer should be 1, 2, 101, 202. Always list all factors, not just some of them.

Can I use a factor tree instead?

Absolutely! A factor tree is another great way to find prime factors. Start with 202, split it into $2 × 101$ , then confirm both 2 and 101 are prime.

What's the difference between factors and prime factors?

Prime factors are the building blocks (2 and 101 for 202). All factors include every number that divides evenly: 1, 2, 101, and 202.

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