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Last updated on May 26th, 2025

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Factors of 4900

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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 4900, how they are used in real life, and tips to learn them quickly.

Factors of 4900 for Indian Students
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What are the Factors of 4900?

The numbers that divide 4900 evenly are known as factors of 4900.

 

A factor of 4900 is a number that divides the number without remainder.

 

The factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 49, 70, 98, 100, 140, 196, 245, 350, 490, 700, 980, 1225, 2450, and 4900.

 

Negative factors of 4900: -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -49, -70, -98, -100, -140, -196, -245, -350, -490, -700, -980, -1225, -2450, and -4900.

 

Prime factors of 4900: 2, 5, and 7. Prime factorization of 4900: (22 times 52 times 72).

 

The sum of factors of 4900: 17280

 

factors of 4900

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How to Find Factors of 4900?

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

 

  • Finding factors using multiplication
     
  • Finding factors using division method
     
  • Prime factors and Prime factorization
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 4900. Identifying the numbers which are multiplied to get the number 4900 is the multiplication method.

 

Step 1: Multiply 4900 by 1, 4900 × 1 = 4900.

 

Step 2: Check for other numbers that give 4900 after multiplying

2 × 2450 = 4900

4 × 1225 = 4900

5 × 980 = 4900

7 × 700 = 4900

10 × 490 = 4900

14 × 350 = 4900

20 × 245 = 4900

25 × 196 = 4900

28 × 175 = 4900

35 × 140 = 4900

49 × 100 = 4900

50 × 98 = 4900

 

Therefore, the positive factor pairs of 4900 are: (1, 4900), (2, 2450), (4, 1225), (5, 980), (7, 700), (10, 490), (14, 350), (20, 245), (25, 196), (28, 175), (35, 140), (49, 100), (50, 98).

 

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 result as whole numbers as factors. Factors can be calculated by following simple division method

 

Step 1: Divide 4900 by 1, 4900 ÷ 1 = 4900.

 

Step 2: Continue dividing 4900 by the numbers until the remainder becomes 0.

4900 ÷ 1 = 4900

4900 ÷ 2 = 2450

4900 ÷ 4 = 1225

4900 ÷ 5 = 980

4900 ÷ 7 = 700

4900 ÷ 10 = 490

4900 ÷ 14 = 350

4900 ÷ 20 = 245

4900 ÷ 25 = 196

4900 ÷ 28 = 175

4900 ÷ 35 = 140

4900 ÷ 49 = 100

4900 ÷ 50 = 98

 

Therefore, the factors of 4900 are: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 49, 70, 98, 100, 140, 196, 245, 350, 490, 700, 980, 1225, 2450, and 4900.

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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
     
  • Using factor tree

 

Using Prime Factorization: In this process, prime factors of 4900 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

4900 ÷ 2 = 2450

2450 ÷ 2 = 1225

1225 ÷ 5 = 245

245 ÷ 5 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

 

The prime factors of 4900 are 2, 5, and 7.

 

The prime factorization of 4900 is: (22 times 52 times 72).

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Factor Tree

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

 

Step 1: Firstly, 4900 is divided by 2 to get 2450.

 

Step 2: Now divide 2450 by 2 to get 1225.

 

Step 3: Then divide 1225 by 5 to get 245.

 

Step 4: Divide 245 by 5 to get 49.

 

Step 5: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 4900 is: (22 times 52 times 72).

 

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 4900: (1, 4900), (2, 2450), (4, 1225), (5, 980), (7, 700), (10, 490), (14, 350), (20, 245), (25, 196), (28, 175), (35, 140), (49, 100), (50, 98).

 

Negative factor pairs of 4900: (-1, -4900), (-2, -2450), (-4, -1225), (-5, -980), (-7, -700), (-10, -490), (-14, -350), (-20, -245), (-25, -196), (-28, -175), (-35, -140), (-49, -100), (-50, -98).

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Common Mistakes and How to Avoid Them in Factors of 4900

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

Mistake 1

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Forgetting the number itself and 1 is a factor

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Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 4900, 1 and 4900 are also factors.

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Factors of 4900 Examples

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Problem 1

A farmer has 4900 apples and wants to pack them in boxes of 100. How many boxes will he need?

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He will need 49 boxes.

Explanation

To find the number of boxes, divide the total apples by the number of apples per box.

4900/100 = 49

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Problem 2

A rectangular garden has an area of 4900 square meters. If the length is 70 meters, what is the width?

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70 meters.

Explanation

To find the width of the garden, use the formula, Area = length × width

4900 = 70 × width

To find the width, move 70 to the left side.

4900/70 = width

Width = 70.

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Problem 3

A company is distributing 4900 fliers equally among 14 locations. How many fliers will each location receive?

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Each location will receive 350 fliers.

Explanation

To find the fliers per location, divide the total fliers by the number of locations.

4900/14 = 350

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Problem 4

A school has 4900 students, and there are 7 grades. How many students are there in each grade?

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There are 700 students in each grade.

Explanation

Dividing the students by the total grades, we get the number of students per grade.

4900/7 = 700

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Problem 5

A library has 4900 books to be arranged in 49 shelves. How many books will go on each shelf?

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Each shelf will have 100 books.

Explanation

Divide the total books by the number of shelves.

4900/49 = 100

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FAQs on Factors of 4900

1.What are the factors of 4900?

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2.Mention the prime factors of 4900.

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3.Is 4900 a multiple of 7?

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4.Mention the factor pairs of 4900?

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5.What is the square of 4900?

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6.How can children in India use numbers in everyday life to understand Factors of 4900?

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7.What are some fun ways kids in India can practice Factors of 4900 with numbers?

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8.What role do numbers and Factors of 4900 play in helping children in India develop problem-solving skills?

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9.How can families in India create number-rich environments to improve Factors of 4900 skills?

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Important Glossaries for Factors of 4900

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 4900 are 1, 2, 4, 5, etc.

 

  • Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 4900.

 

  • 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 4900 are (1, 4900), (2, 2450), etc.

 

  • Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of 4900 is (22 times 52 times 72).

 

  • Negative factors: Factors that are negative numbers. For example, -1, -2, -4, and so on, are negative factors of 4900.
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About BrightChamps in India

At BrightChamps, numbers mean more than just digits—they open pathways to endless opportunities! We’re here to help children all over India grasp crucial math skills, focusing on today’s Factors of 4900 with a special look at factors—in a way that’s enjoyable, simple, and interactive. Whether your child is calculating the speed of a train passing by, following scores in a cricket match, or managing their pocket money for new gadgets, knowing numbers helps build their confidence in daily life. Our hands-on lessons keep learning fun and easy. Since kids in India learn in many ways, we customize lessons to fit each learner. From Mumbai’s lively markets to Delhi’s vibrant streets, BrightChamps makes math meaningful and exciting all across India. Let’s turn factors into a fun part of every child’s math story!
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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.

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Fun Fact

: She loves to read number jokes and games.

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