List All the Factors of Number 500: A Step-by-Step Approach

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

Factors are all numbers that divide evenly into 500 (like 1, 2, 4, 5, 10, 20...). Prime factors are only the prime numbers used in multiplication: 2, 2, 5, 5, 5.

Q: Why do I write 5 three times instead of just once?

Because 500 contains three copies of the prime 5! Writing $ 5^3 $ shows the exponent, but listing them shows exactly how many times each prime appears.

Q: Do I always start with 2?

Start with 2 only if the number is even. If it's odd, try 3, then 5, then 7, and so on. Always use the smallest possible prime at each step.

Prime Factorization with Composite Numbers

Write all the factors of the following number: $500$

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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.

00:07 Since the last digit is zero, two is a prime factor.

00:13 Divide by two. Then use the result to find more factors.

00:17 Again, the last digit is zero. So, two is still a prime factor.

00:22 Let's divide by two again and find more factors.

00:26 This time, the last digit is five. So, five is a prime factor.

00:32 Divide by five. Next, keep going to find more factors.

00:36 Once more, the last digit is five. So, five is again a factor.

00:42 Divide by five. And look for additional factors.

00:46 Now, our result is a prime number. It's a factor by itself.

00:51 And that's how we 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: $500$

Step-by-step solution

Let's solve the problem step-by-step by performing prime factorization:

Step 1: Begin with the number 500. The smallest prime number is 2, and 500 is even, so divide 500 by 2.
$500 \div 2 = 250$ . Now, 250 is still even, divide again by 2.
$250 \div 2 = 125$ . At this point, 125 is not divisible by 2 but by 5.
$125 \div 5 = 25$ . Continue with division by 5 as 25 is divisible by 5.
$25 \div 5 = 5$ . Finally, divide by 5 to get 1.
The prime factors of 500 are therefore 2, 2, 5, 5, and 5.

Thus, the complete prime factorization of 500 is $2^2 \times 5^3$ .

Consequently, these prime factors in multiplicity form are $5, 5, 5, 2, 2$ .

Final Answer

$5,5,5,2,2$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide by smallest prime until you reach 1
Technique: Start with 2 for even numbers: 500 ÷ 2 = 250
Check: Multiply all factors: 2 × 2 × 5 × 5 × 5 = 500 ✓

Common Mistakes

Avoid these frequent errors

Confusing factors with prime factors
Don't list all factors like 1, 2, 4, 5, 10... = wrong answer! The question asks for prime factors only, not all divisors. Always break the number down using only prime numbers (2, 3, 5, 7, 11...) until you reach 1.

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 500 (like 1, 2, 4, 5, 10, 20...). Prime factors are only the prime numbers used in multiplication: 2, 2, 5, 5, 5.

Why do I write 5 three times instead of just once?

Because 500 contains three copies of the prime 5! Writing $5^3$ shows the exponent, but listing them shows exactly how many times each prime appears.

Do I always start with 2?

Start with 2 only if the number is even. If it's odd, try 3, then 5, then 7, and so on. Always use the smallest possible prime at each step.

How do I know when I'm done?

You're finished when your final division gives you 1. If you end with any number greater than 1, keep factoring that number too!

What if I get stuck on a big number?

Try dividing by small primes systematically: 2, 3, 5, 7, 11, 13... Use a calculator if needed, but keep going until you reach 1.

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