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 4500, how they are used in real life, and tips to learn them quickly.
The numbers that divide 4500 evenly are known as factors of 4500. A factor of 4500 is a number that divides the number without remainder. The factors of 4500 include 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 250, 300, 450, 500, 750, 900, 1500, 2250, and 4500. Negative factors of 4500: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -150, -180, -225, -250, -300, -450, -500, -750, -900, -1500, -2250, and -4500. Prime factors of 4500: 2, 3, and 5. Prime factorization of 4500: 2^2 × 3^2 × 5^3. The sum of factors of 4500: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 250 + 300 + 450 + 500 + 750 + 900 + 1500 + 2250 + 4500 = 12696.
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 4500. Identifying the numbers which are multiplied to get the number 4500 is the multiplication method.
Step 1: Multiply 4500 by 1, 4500 × 1 = 4500.
Step 2: Check for other numbers that give 4500 after multiplying
2 × 2250 = 4500
3 × 1500 = 4500
5 × 900 = 4500
6 × 750 = 4500
9 × 500 = 4500
10 × 450 = 4500
12 × 375 = 4500
15 × 300 = 4500
18 × 250 = 4500
20 × 225 = 4500
25 × 180 = 4500
30 × 150 = 4500
36 × 125 = 4500
45 × 100 = 4500
50 × 90 = 4500
60 × 75 = 4500
Therefore, the positive factor pairs of 4500 are: (1, 4500), (2, 2250), (3, 1500), (5, 900), (6, 750), (9, 500), (10, 450), (12, 375), (15, 300), (18, 250), (20, 225), (25, 180), (30, 150), (36, 125), (45, 100), (50, 90), and (60, 75).
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 a simple division method
Step 1: Divide 4500 by 1, 4500 ÷ 1 = 4500.
Step 2: Continue dividing 4500 by the numbers until the remainder becomes 0.
4500 ÷ 1 = 4500
4500 ÷ 2 = 2250
4500 ÷ 3 = 1500
4500 ÷ 5 = 900
4500 ÷ 6 = 750
4500 ÷ 9 = 500
4500 ÷ 10 = 450
4500 ÷ 12 = 375
4500 ÷ 15 = 300
4500 ÷ 18 = 250
4500 ÷ 20 = 225
4500 ÷ 25 = 180
4500 ÷ 30 = 150
4500 ÷ 36 = 125
4500 ÷ 45 = 100
4500 ÷ 50 = 90
4500 ÷ 60 = 75
Therefore, the factors of 4500 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 250, 300, 450, 500, 750, 900, 1500, 2250, and 4500.
The factors can be found by dividing by prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 4500 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
4500 ÷ 2 = 2250
2250 ÷ 2 = 1125
1125 ÷ 3 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 4500 are 2, 3, and 5.
The prime factorization of 4500 is: 22 × 32 × 53.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 4500 is divided by 2 to get 2250.
Step 2: Now divide 2250 by 2 to get 1125.
Step 3: Then divide 1125 by 3 to get 375.
Step 4: Divide 375 by 3 to get 125.
Step 5: Divide 125 by 5 to get 25.
Step 6: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 4500 is: 22 × 32 × 53.
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 4500: (1, 4500), (2, 2250), (3, 1500), (5, 900), (6, 750), (9, 500), (10, 450), (12, 375), (15, 300), (18, 250), (20, 225), (25, 180), (30, 150), (36, 125), (45, 100), (50, 90), and (60, 75).
Negative factor pairs of 4500: (-1, -4500), (-2, -2250), (-3, -1500), (-5, -900), (-6, -750), (-9, -500), (-10, -450), (-12, -375), (-15, -300), (-18, -250), (-20, -225), (-25, -180), (-30, -150), (-36, -125), (-45, -100), (-50, -90), and (-60, -75).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and ways to avoid them.
There are 90 students and 4500 pencils. How will they divide them equally?
They will get 50 pencils each.
To divide the pencils equally, we need to divide the total pencils by the number of students.
4500/90 = 50
A plot is rectangular, the length of the plot is 50 meters, and the total area is 4500 square meters. Find the width?
90 meters.
To find the width of the plot, we use the formula, Area = length × width
4500 = 50 × width
To find the value of width, we need to divide 4500 by 50.
4500/50 = width
Width = 90.
There are 75 gift bags and 4500 candies. How many candies will be in each bag?
Each bag will have 60 candies.
To find the candies in each bag, divide the total candies by the number of bags.
4500/75 = 60
In a factory, there are 4500 pieces of equipment, and they need to be packed in 100 boxes. How many pieces will be there in each box?
There will be 45 pieces in each box.
Dividing the equipment by the total boxes, we will get the number of pieces in each box.
4500/100 = 45
4500 chairs need to be arranged in 225 rows. How many chairs will go in each row?
Each row will have 20 chairs.
Divide total chairs by rows.
4500/225 = 20
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.