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 1350, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1350 evenly are known as factors of 1350.
A factor of 1350 is a number that divides the number without remainder.
The factors of 1350 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, and 1350.
Negative factors of 1350: -1, -2, -3, -5, -6, -9, -10, -15, -18, -25, -27, -30, -45, -50, -54, -75, -90, -135, -150, -225, -270, -450, -675, and -1350.
Prime factors of 1350: 2, 3, and 5.
Prime factorization of 1350: 2 × 33 × 52.
The sum of the factors of 1350: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 25 + 27 + 30 + 45 + 50 + 54 + 75 + 90 + 135 + 150 + 225 + 270 + 450 + 675 + 1350 = 3726
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 1350. Identifying the numbers which are multiplied to get the number 1350 is the multiplication method.
Step 1: Multiply 1350 by 1, 1350 × 1 = 1350.
Step 2: Check for other numbers that give 1350 after multiplying
2 × 675 = 1350
3 × 450 = 1350
5 × 270 = 1350
6 × 225 = 1350
9 × 150 = 1350
10 × 135 = 1350
15 × 90 = 1350
18 × 75 = 1350
25 × 54 = 1350
27 × 50 = 1350
30 × 45 = 1350
Therefore, the positive factor pairs of 1350 are: (1, 1350), (2, 675), (3, 450), (5, 270), (6, 225), (9, 150), (10, 135), (15, 90), (18, 75), (25, 54), (27, 50), (30, 45).
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 1350 by 1, 1350 ÷ 1 = 1350.
Step 2: Continue dividing 1350 by the numbers until the remainder becomes 0.
1350 ÷ 1 = 1350
1350 ÷ 2 = 675
1350 ÷ 3 = 450
1350 ÷ 5 = 270
1350 ÷ 6 = 225
1350 ÷ 9 = 150
1350 ÷ 10 = 135
1350 ÷ 15 = 90
1350 ÷ 18 = 75
1350 ÷ 25 = 54
1350 ÷ 27 = 50
1350 ÷ 30 = 45
Therefore, the factors of 1350 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350.
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 1350 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1350 ÷ 2 = 675
675 ÷ 3 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 1350 are 2, 3, and 5.
The prime factorization of 1350 is: 2 × 33 × 52.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1350 is divided by 2 to get 675.
Step 2: Now divide 675 by 3 to get 225.
Step 3: Then divide 225 by 3 to get 75.
Step 4: Divide 75 by 3 to get 25.
Step 5: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1350 is: 2 × 33 × 52.
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 1350: (1, 1350), (2, 675), (3, 450), (5, 270), (6, 225), (9, 150), (10, 135), (15, 90), (18, 75), (25, 54), (27, 50), and (30, 45).
Negative factor pairs of 1350: (-1, -1350), (-2, -675), (-3, -450), (-5, -270), (-6, -225), (-9, -150), (-10, -135), (-15, -90), (-18, -75), (-25, -54), (-27, -50), and (-30, -45).
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 garden has 450 flowers and needs to be divided into 15 equal sections. How many flowers will be in each section?
Each section will have 30 flowers.
To divide the flowers equally, we need to divide the total flowers by the number of sections.
450/15 = 30
A rectangular piece of land has a length of 10 meters and a total area of 1350 square meters. Find the width?
135 meters.
To find the width of the land, we use the formula,
Area = length × width
1350 = 10 × width
To find the value of width, we need to shift 10 to the left side.
1350/10 = width
Width = 135.
There are 225 apples to be packed into boxes, with each box holding 25 apples. How many boxes are needed?
9 boxes are needed.
To find the number of boxes needed, divide the total apples by the number of apples per box.
225/25 = 9
An event has 90 guests, and the seating is arranged in 15 tables. How many guests will sit at each table?
There are 6 guests at each table.
Dividing the guests by the total tables, we will get the number of guests at each table.
90/15 = 6
1350 books need to be distributed equally among 45 students. How many books will each student receive?
Each student will receive 30 books.
Divide total books by the number of students.
1350/45 = 30
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.