Factors of 1250
2026-02-28 13:03 Diff

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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1250, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1250?

The numbers that divide 1250 evenly are known as factors of 1250. A factor of 1250 is a number that divides the number without remainder. The factors of 1250 are 1, 2, 5, 10, 25, 50, 125, 250, 625, and 1250.

Negative factors of 1250: -1, -2, -5, -10, -25, -50, -125, -250, -625, and -1250.

Prime factors of 1250: 2 and 5.

Prime factorization of 1250: 2 × 54.

The sum of factors of 1250: 1 + 2 + 5 + 10 + 25 + 50 + 125 + 250 + 625 + 1250 = 2343

How to Find Factors of 1250?

Factors can be found using different methods. Mentioned below are some commonly used methods:

  1. Finding factors using multiplication
  2. Finding factors using division method
  3. Prime factors and Prime factorization

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1250. Identifying the numbers which are multiplied to get the number 1250 is the multiplication method.

Step 1: Multiply 1250 by 1, 1250 × 1 = 1250.

Step 2: Check for other numbers that give 1250 after multiplying     

2 × 625 = 1250    

 5 × 250 = 1250     

10 × 125 = 1250    

 25 × 50 = 1250

Therefore, the positive factor pairs of 1250 are: (1, 1250), (2, 625), (5, 250), (10, 125), (25, 50). All these factor pairs result in 1250. For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which results as whole numbers as factors. Factors can be calculated by following simple division method -

Step 1: Divide 1250 by 1, 1250 ÷ 1 = 1250.

Step 2: Continue dividing 1250 by the numbers until the remainder becomes 0.

1250 ÷ 1 = 1250

1250 ÷ 2 = 625

1250 ÷ 5 = 250

1250 ÷ 10 = 125

1250 ÷ 25 = 50

Therefore, the factors of 1250 are: 1, 2, 5, 10, 25, 50, 125, 250, 625, 1250.

Prime Factors and Prime Factorization

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of 1250 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1250 ÷ 2 = 625

625 ÷ 5 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

The prime factors of 1250 are 2 and 5. The prime factorization of 1250 is: 2 × 54.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 1250 is divided by 2 to get 625.

Step 2: Now divide 625 by 5 to get 125.

Step 3: Then divide 125 by 5 to get 25.

Step 4: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1250 is: 2 × 54.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

  • Positive factor pairs of 1250: (1, 1250), (2, 625), (5, 250), (10, 125), and (25, 50).
  • Negative factor pairs of 1250: (-1, -1250), (-2, -625), (-5, -250), (-10, -125), and (-25, -50).

Common Mistakes and How to Avoid Them in Factors of 1250

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 5 boxes and 1250 marbles. How will they divide it equally?

Okay, lets begin

They will get 250 marbles each.

Explanation

To divide the marbles equally, we need to divide the total marbles with the number of boxes

1250/5 = 250

Well explained 👍

Problem 2

A rectangular garden has a length of 25 meters and a total area of 1250 square meters. Find the width?

Okay, lets begin

50 meters.

Explanation

To find the width of the garden, we use the formula,     

Area = length × width     

1250 = 25 × width     

To find the value of width, we need to shift 25 to the left side.     

1250/25 = width     

Width = 50.

Well explained 👍

Problem 3

There are 10 sacks and 1250 kilograms of rice. How many kilograms will be in each sack?

Okay, lets begin

Each sack will have 125 kilograms.

Explanation

To find the rice in each sack, divide the total kilograms by the number of sacks.     

1250/10 = 125

Well explained 👍

Problem 4

In a class, there are 1250 students, and 250 groups. How many students are there in each group?

Okay, lets begin

There are 5 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.     

1250/250 = 5

Well explained 👍

Problem 5

1250 books need to be arranged in 5 bookshelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 250 books.

Explanation

Divide total books by the number of shelves.     

1250/5 = 250

Well explained 👍

FAQs on Factors of 1250

1.What are the factors of 1250?

1, 2, 5, 10, 25, 50, 125, 250, 625, 1250 are the factors of 1250.

2.Mention the prime factors of 1250.

The prime factors of 1250 are 2 × 5^4.

3.Is 1250 a multiple of 25?

4.Mention the factor pairs of 1250?

(1, 1250), (2, 625), (5, 250), (10, 125), and (25, 50) are the factor pairs of 1250.

5.What is the square of 1250?

The square of 1250 is 1,562,500.

Important Glossaries for Factor of 1250

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1250 are 1, 2, 5, 10, 25, 50, 125, 250, 625, and 1250.
  • Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 1250.
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1250 are (1, 1250), (2, 625), etc.
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1250 is 2 × 54.
  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number. For example, the pairs for 1250 are (1, 1250), (2, 625), etc.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.