124 LearnersLast updated on May 26th, 2025
Factors of 1028
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1028, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1028?
The numbers that divide 1028 evenly are known as factors of 1028.
A factor of 1028 is a number that divides the number without remainder.
The factors of 1028 are 1, 2, 4, 257, 514, and 1028.
Negative factors of 1028: -1, -2, -4, -257, -514, and -1028.
Prime factors of 1028: 2 and 257.
Prime factorization of 1028: 2² × 257.
The sum of factors of 1028: 1 + 2 + 4 + 257 + 514 + 1028 = 1806
How to Find Factors of 1028?
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 1028. Identifying the numbers which are multiplied to get the number 1028 is the multiplication method.
Step 1: Multiply 1028 by 1, 1028 × 1 = 1028.
Step 2: Check for other numbers that give 1028 after multiplying
2 × 514 = 1028
4 × 257 = 1028
Therefore, the positive factor pairs of 1028 are: (1, 1028), (2, 514), and (4, 257). All these factor pairs result in 1028. 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 simple division method -
Step 1: Divide 1028 by 1, 1028 ÷ 1 = 1028.
Step 2: Continue dividing 1028 by the numbers until the remainder becomes 0.
1028 ÷ 1 = 1028
1028 ÷ 2 = 514
1028 ÷ 4 = 257
Therefore, the factors of 1028 are: 1, 2, 4, 257, 514, and 1028.
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 1028 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1028 ÷ 2 = 514
514 ÷ 2 = 257
257 ÷ 257 = 1
The prime factors of 1028 are 2 and 257.
The prime factorization of 1028 is: 2² × 257.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1028 is divided by 2 to get 514.
Step 2: Now divide 514 by 2 to get 257.
Here, 257 is a prime number that cannot be divided anymore.
So, the prime factorization of 1028 is: 2² × 257.
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 1028: (1, 1028), (2, 514), and (4, 257).
Negative factor pairs of 1028: (-1, -1028), (-2, -514), and (-4, -257).
Common Mistakes and How to Avoid Them in Factors of 1028
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 1028, 1 and 1028 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1028 consist of -1, -2, -4, 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 3.5 as a factor, because 1028/3.5 = 293.714, 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 1028 are prime numbers.
For example, 2 and 257 are the prime factors of 1028, but it has other factors like 4, 514.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1028 as 2² × 257 and missing all the key factors.
Factors of 1028 Examples
Problem 1
A charity has 1028 donation boxes and 4 different centers. How many boxes will each center receive if distributed equally?
Each center will receive 257 boxes.
Explanation
To distribute the donation boxes equally, we need to divide the total boxes by the number of centers.
1028/4 = 257
Problem 2
A rectangular garden has a length of 514 meters and an area of 1028 square meters. What is the width of the garden?
2 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1028 = 514 × width
To find the value of width, we need to shift 514 to the left side.
1028/514 = width
Width = 2.
Problem 3
A baker has 1028 cupcakes and wants to pack them into boxes, with each box holding 2 cupcakes. How many boxes will the baker need?
The baker will need 514 boxes.
Explanation
To find the number of boxes needed, divide the total cupcakes by the number each box can hold.
1028/2 = 514
Problem 4
A school has 1028 students and wants to form 257 equal-sized teams. How many students will be in each team?
There will be 4 students in each team.
Explanation
Dividing the students by the total number of teams, we get the number of students per team.
1028/257 = 4
Problem 5
A library has 1028 books and wants to arrange them in 2 books per shelf. How many shelves will be needed?
The library will need 514 shelves.
Explanation
Divide total books by books per shelf. 1028/2 = 514
FAQs on Factors of 1028
1.What are the factors of 1028?
2.Mention the prime factors of 1028.
3.Is 1028 a multiple of 4?
4.Mention the factor pairs of 1028?
5.What is the square of 1028?
Important Glossaries for Factor of 1028
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1028 are 1, 2, 4, 257, 514, and 1028.
- Prime factors: The factors which are prime numbers. For example, 2 and 257 are prime factors of 1028.
- 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 1028 are (1, 1028), (2, 514), and (4, 257).
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 1028 = 2² × 257.
- Negative factors: Factors that are negative counterparts of the positive factors. For example, -1, -2, -4, -257, -514, and -1028 are negative factors of 1028.
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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
: She loves to read number jokes and games.
