125 LearnersLast updated on May 26th, 2025
Factors of 1350
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.
What are the Factors of 1350?
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
How to Find Factors of 1350?
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 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.
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 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.
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 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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 1350
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 the factors for every word.Always remember to include 1 and the number itself.
For example, in factors of 1350, 1 and 1350 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 1350 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1350/1.5 ≈ 900, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 1350 are prime numbers. For instance, 2, 3, and 5 are the prime factors of 1350, but it has other factors like 6, 45.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 1350 as 2 × 3^3 × 5^2 and missing all the key factors.
Factors of 1350 Examples
Problem 1
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.
Explanation
To divide the flowers equally, we need to divide the total flowers by the number of sections.
450/15 = 30
Problem 2
A rectangular piece of land has a length of 10 meters and a total area of 1350 square meters. Find the width?
135 meters.
Explanation
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.
Problem 3
There are 225 apples to be packed into boxes, with each box holding 25 apples. How many boxes are needed?
9 boxes are needed.
Explanation
To find the number of boxes needed, divide the total apples by the number of apples per box.
225/25 = 9
Problem 4
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.
Explanation
Dividing the guests by the total tables, we will get the number of guests at each table.
90/15 = 6
Problem 5
1350 books need to be distributed equally among 45 students. How many books will each student receive?
Each student will receive 30 books.
Explanation
Divide total books by the number of students.
1350/45 = 30
FAQs on Factors of 1350
1.What are the factors of 1350?
2.Mention the prime factors of 1350.
3.Is 1350 a multiple of 9?
4.Mention the factor pairs of 1350?
5.What is the square of 1350?
6.How can children in Canada use numbers in everyday life to understand Factors of 1350?
7.What are some fun ways kids in Canada can practice Factors of 1350 with numbers?
8.What role do numbers and Factors of 1350 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1350 skills?
Important Glossaries for Factor of 1350
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1350 are 1, 2, 3, 5, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 1350.
- 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 1350 are (1, 1350), (2, 675), etc.
- Prime factorization: A method of expressing a number as a product of its prime factors. For example, the prime factorization of 1350 is 2 × 33 × 52.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1350 is a multiple of 9.
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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.
Fun Fact
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