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 = 2² × 5³

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  = 2² × 5³

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?

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.