128 LearnersLast updated on May 26th, 2025
Factors of 1026
Factors are the numbers that divide any given number evenly without a 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 1026, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1026?
The numbers that divide 1026 evenly are known as factors of 1026.
A factor of 1026 is a number that divides the number without a remainder.
The factors of 1026 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 57, 54, 114, 171, 342, 513, and 1026.
Negative factors of 1026: -1, -2, -3, -6, -9, -18, -19, -27, -38, -57, -54, -114, -171, -342, -513, and -1026.
Prime factors of 1026: 2, 3, and 19.
Prime factorization of 1026: 2 × 33 × 19.
The sum of factors of 1026: 1 + 2 + 3 + 6 + 9 + 18 + 19 + 27 + 38 + 57 + 54 + 114 + 171 + 342 + 513 + 1026 = 2400
How to Find Factors of 1026?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1026. Identifying the numbers which are multiplied to get the number 1026 is the multiplication method.
Step 1: Multiply 1026 by 1, 1026 × 1 = 1026.
Step 2: Check for other numbers that give 1026 after multiplying
2 × 513 = 1026
3 × 342 = 1026
6 × 171 = 1026
9 × 114 = 1026
18 × 57 = 1026
19 × 54 = 1026
27 × 38 = 1026
Therefore, the positive factor pairs of 1026 are: (1, 1026), (2, 513), (3, 342), (6, 171), (9, 114), (18, 57), (19, 54), (27, 38). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 1026 by 1, 1026 ÷ 1 = 1026.
Step 2: Continue dividing 1026 by the numbers until the remainder becomes 0.
1026 ÷ 1 = 1026
1026 ÷ 2 = 513
1026 ÷ 3 = 342
1026 ÷ 6 = 171
1026 ÷ 9 = 114
1026 ÷ 18 = 57
1026 ÷ 19 = 54
1026 ÷ 27 = 38
Therefore, the factors of 1026 are: 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 114, 171, 342, 513, 1026.
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 1026 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1026 ÷ 2 = 513
513 ÷ 3 = 171
171 ÷ 3 = 57
57 ÷ 3 = 19
19 ÷ 19 = 1
The prime factors of 1026 are 2, 3, and 19.
The prime factorization of 1026 is: 2 × 3^3 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1026 is divided by 2 to get 513.
Step 2: Now divide 513 by 3 to get 171.
Step 3: Then divide 171 by 3 to get 57.
Step 4: Divide 57 by 3 to get 19. Here, 19 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1026 is: 2 × 33 × 19.
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 1026: (1, 1026), (2, 513), (3, 342), (6, 171), (9, 114), (18, 57), (19, 54), and (27, 38).
Negative factor pairs of 1026: (-1, -1026), (-2, -513), (-3, -342), (-6, -171), (-9, -114), (-18, -57), (-19, -54), and (-27, -38).
Common Mistakes and How to Avoid Them in Factors of 1026
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 number. Always remember to include 1 and the number itself.
For example, in factors of 1026, 1 and 1026 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors
. For example, the factors of 1026 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 1026/1.5 = 684, which is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, thinking all the factors of 1026 are prime numbers. While 2, 3, and 19 are the prime factors of 1026, it has other factors like 6, 9, 54.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing incorrect factors.
For example, not breaking 1026 as 2 × 3^3 × 19 and missing key factors.
Factors of 1026 Examples
Problem 1
A company has 1026 chairs to distribute equally among 18 offices. How many chairs will each office receive?
Each office will receive 57 chairs.
Explanation
To divide the chairs equally, divide the total chairs by the number of offices.
1026/18 = 57
Problem 2
A stadium has a total area of 1026 square meters. If the length of the stadium is 38 meters, find the width.
27 meters.
Explanation
To find the width of the stadium, use the formula:
Area = length × width
1026 = 38 × width
To find the width, divide 1026 by 38.
1026/38 = 27
Problem 3
A factory produces 1026 gadgets, and they are packed in boxes with 9 gadgets each. How many boxes are needed?
114 boxes are needed.
Explanation
To find the number of boxes, divide the total gadgets by the number of gadgets per box.
1026/9 = 114
Problem 4
A library has 1026 books, which need to be placed in 57 shelves. How many books will be on each shelf?
There will be 18 books on each shelf.
Explanation
Divide the total books by the number of shelves to find the number of books on each shelf.
1026/57 = 18
Problem 5
1026 students are to be divided into 6 groups for a workshop. How many students will be in each group?
Each group will have 171 students.
Explanation
Divide the total number of students by the number of groups to find the number of students in each group.
1026/6 = 171
FAQs on Factors of 1026
1.What are the factors of 1026?
2.Mention the prime factors of 1026.
3.Is 1026 a multiple of 9?
4.Mention the factor pairs of 1026?
5.What is the square of 1026?
6.How can children in United States use numbers in everyday life to understand Factors of 1026?
7.What are some fun ways kids in United States can practice Factors of 1026 with numbers?
8.What role do numbers and Factors of 1026 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1026 skills?
Important Glossaries for Factors of 1026
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1026 are 1, 2, 3, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 19 are prime factors of 1026.
- 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 1026 are (1, 1026), (2, 513), etc.
- Prime factorization: Breaking down a number into a product of prime numbers. For example, the prime factorization of 1026 is 2 × 33 × 19.
- Multiple: A number that can be divided by another number without a remainder. For example, 1026 is a multiple of 9.
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About BrightChamps in United States
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.
