Factors of 500
Factors of 500 are the integers which when multiplied in pairs give the product as 500. Factors of 500 have a total of 12 factors in all and a total of 6 positive and negative factor pairs as well. In this lesson, we will calculate the factors of 500, the prime factors of 500, and the factors of 500 in pairs. We will also solve problems related to the factors of 500.
 Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.
 Prime Factorization of 500: 500 = 2^{2} × 5^{3}
What Are the Factors of 500?
Before we learn about factors of 500, let us learn about factors. Factors of 500 are the numbers which give the value 500 when they are multiplied. The factors of 500 are the numbers which divide it without leaving any remainder. So, when any two whole numbers are multiplied with each other and 500 is obtained as the answer, it is said that both these numbers are the factors of 500.
Let's learn how to calculate the factors of 500.
 Step 1: Write down the number to be factored. The number to be factored is 500.
 Step 2: Find the two numbers whose product gives 500.
The product of the numbers which results in 500 are 2 and 250, 100 and 5 and so on. Hence, the factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.
Explore factors using illustrations and interactive examples
 Factors of 25  The factors of 25 are 1, 5, and 25.
 Factors of 125  The factors of 125 are 1, 5, 25, and 125.
 Factors of 250  The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250.
 Factors of 54  The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
 Factors of 150  The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150
 Factors of 450  The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225
, and 450
Prime factorization means expressing a number in terms of the product of its prime factors. We can do use the upside division method or factor tree to do this.
1. Prime Factorization by Upside Division method
The number 500 is divided by the smallest prime number which divides 500 exactly, i.e. it leaves a remainder 0. The quotient is then divided by the smallest or second smallest prime number and the process continues till the quotient becomes indivisible.
Since 500 is an even, it will be divisible by 2 and its multiples.
Let us divide 500 by the prime number 2
 500 ÷ 2 = 250
250 is again even, let's again divide by 2
 250 ÷ 2 = 125
This process is repeated till we get the quotient as 1.
The prime factorization of 500 shown below:
Prime factorization of 500 = 2 × 2 × 5 × 5^{ } × 5^{ }= 2^{2} × 5^{3}
2. Prime Factorization by Factor Tree
The other way of prime factorization as taking 500 as the root, we create branches by dividing it by prime numbers. This method is similar to above division method. The difference lies in presenting the factorization.
The figure below shows the factor tree of 500. The composite numbers will have branches as they are further divisible. We continue making branches till we are left with only prime numbers.
The numbers inside the circles are the prime factors of 500. Hence, the prime factors of 500 are 2 and 5.
Factors of 500 in Pairs
The pair factors of 500 can be given as below:
 1 × 500 = 500
 2 × 250 = 500
 4 × 125 = 500
 5 × 100 = 500
 10 × 50 = 500
 20 × 25 = 500
The positive pair factors of 500 are (1, 500), (2, 250), (4, 125), (5, 100), (10, 50), (20, 25). It is possible to have negative pair factors as well because the product of two negative numbers gives a positive number. Let's take a look at the negative pair factors of 500.
 1 × 500 = 500
 2 × 250 = 500
 4 × 125 = 500
 5 × 100 = 500
 10 × 50 = 500
 20 × 25 = 500
The negative pair factors of 500 are (1, 500), (2, 250), (4, 125), (5, 100), (10, 50), (20, 25).
Important Notes:
 1 is the smallest factor of every number. Hence, 1 is a factor of 500.
 500 is not a perfect square number. Thus, it has an even number of factors.
 500 is an even number; hence, 2 is one of their factors.
Challenging Questions:
 Christopher has 2 books with 500 pages each. If it takes him 1 hour to write 1 page in any book, how much time would it take for him to fill 10 such books?
 How will Julia divide $500 equally between 4 of her friends?
Factors of 500 Solved Examples

Example 1: Adaline owns a bakery shop. Her store is known for its delicious cakes. Customer placed an order for 4 cakes to be made. If the cost of 1 cake is $125. Find the cost of 4 cakes.
Solution:
Total number of cakes to be bake = 4
Cost of 1 cake = $125
Cost of 4 cakes = $125 × 4 = $500. 
Example 2: John owns a grocery shop. A customer purchased five packets of noodles from him. If the total bill was $500, how much did the customer pay for each packet of noodles?
Solution:
The customer's bill was $500.
The customer purchased 5 packets of noodles from the grocery shop.
500 ÷ 5 = 100
So, each packet costs $100.
Hence, the customer bought each packet of noodles for $100. 
Example 3: Jack asked his friend to name any two factors of 500 within 30 seconds. Jack's friend thought and immediately gave him two factors of 500. What could be those two factors?
Solution:
Every number will definitely have a minimum of two factors, 1 and itself.
So, without thinking too much, we can say that 1 and 500 are the factors of 500.
Hence, the two factors of 500 that Jack's friend mentioned are probably 1 and 500.
FAQs on Factors of 500
What are the factors of 500?
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.
What is the highest factor of 500?
The highest factor of 500 is 500.
What are the prime factors of 500?
The prime factors of 500 are 2 and 5.
Which factor of 500 is a perfect square?
100 is a perfect square factor of 500.
What are the common factors of 500 and 300?
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, and 500.
Thus, the common factors are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
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