124 LearnersLast updated on May 26th, 2025
Factors of 4900
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.
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
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
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.
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.
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).
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).
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
Forgetting the number itself and 1 is a factor
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.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 4900 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 2.5 as a factor, because 4900/2.5 = 1960, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 4900 are prime numbers.
For example, 2, 5, and 7 are the prime factors of 4900, but it has other factors like 4, 28.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 4900 as (22 times 52 times 72) and missing all the key factors.
Factors of 4900 Examples
Problem 1
A farmer has 4900 apples and wants to pack them in boxes of 100. How many boxes will he need?
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
Problem 2
A rectangular garden has an area of 4900 square meters. If the length is 70 meters, what is the width?
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.
Problem 3
A company is distributing 4900 fliers equally among 14 locations. How many fliers will each location receive?
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
Problem 4
A school has 4900 students, and there are 7 grades. How many students are there in each grade?
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
Problem 5
A library has 4900 books to be arranged in 49 shelves. How many books will go on each shelf?
Each shelf will have 100 books.
Explanation
Divide the total books by the number of shelves.
4900/49 = 100
FAQs on Factors of 4900
1.What are the factors of 4900?
2.Mention the prime factors of 4900.
3.Is 4900 a multiple of 7?
4.Mention the factor pairs of 4900?
5.What is the square of 4900?
6.How can children in India use numbers in everyday life to understand Factors of 4900?
7.What are some fun ways kids in India can practice Factors of 4900 with numbers?
8.What role do numbers and Factors of 4900 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 4900 skills?
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.
Explore More numbers
About BrightChamps in India
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.
