Last updated on May 26th, 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 4900, how they are used in real life, and tips to learn them quickly.
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 can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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 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).
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To find the number of boxes, divide the total apples by the number of apples per box.
4900/100 = 49
A rectangular garden has an area of 4900 square meters. If the length is 70 meters, what is the width?
70 meters.
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.
A company is distributing 4900 fliers equally among 14 locations. How many fliers will each location receive?
Each location will receive 350 fliers.
To find the fliers per location, divide the total fliers by the number of locations.
4900/14 = 350
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.
Dividing the students by the total grades, we get the number of students per grade.
4900/7 = 700
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.
Divide the total books by the number of shelves.
4900/49 = 100
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.
: She loves to read number jokes and games.