119 LearnersLast updated on May 26th, 2025
Factors of 1052
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 1052, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1052?
The numbers that divide 1052 evenly are known as factors of 1052.
A factor of 1052 is a number that divides the number without remainder.
The factors of 1052 are 1, 2, 4, 263, 526, and 1052.
Negative factors of 1052: -1, -2, -4, -263, -526, and -1052.
Prime factors of 1052: 2 and 263.
Prime factorization of 1052: 2² × 263.
The sum of factors of 1052: 1 + 2 + 4 + 263 + 526 + 1052 = 1848
How to Find Factors of 1052?
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 1052. Identifying the numbers which are multiplied to get the number 1052 is the multiplication method.
Step 1: Multiply 1052 by 1, 1052 × 1 = 1052.
Step 2: Check for other numbers that give 1052 after multiplying
2 × 526 = 1052
4 × 263 = 1052
Therefore, the positive factor pairs of 1052 are: (1, 1052), (2, 526), (4, 263). All these factor pairs result in 1052. 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 1052 by 1, 1052 ÷ 1 = 1052.
Step 2: Continue dividing 1052 by the numbers until the remainder becomes 0.
1052 ÷ 1 = 1052
1052 ÷ 2 = 526
1052 ÷ 4 = 263
Therefore, the factors of 1052 are: 1, 2, 4, 263, 526, 1052.
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 1052 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1052 ÷ 2 = 526
526 ÷ 2 = 263
263 ÷ 263 = 1
The prime factors of 1052 are 2 and 263.
The prime factorization of 1052 is: 2² × 263.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1052 is divided by 2 to get 526.
Step 2: Now divide 526 by 2 to get 263. Step 3: Here, 263 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1052 is: 2² × 263
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 1052: (1, 1052), (2, 526), (4, 263).
Negative factor pairs of 1052: (-1, -1052), (-2, -526), (-4, -263).
Common Mistakes and How to Avoid Them in Factors of 1052
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 1052, 1 and 1052 is also a factor.
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 1052 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 1.5 as a factor, because 1052/1.5 = 701.333, 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 1052 are prime numbers.
For example, 2 and 263 are the prime factors of 1052, but it has other factors like 4, 526.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 1052 as 2² × 263 and missing all the key factors.
Factors of 1052 Examples
Problem 1
There are 263 students and 1052 pencils. How will they divide it equally?
They will get 4 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of students.
1052/263 = 4
Problem 2
A rectangular garden has a length of 4 meters, and the total area is 1052 square meters. Find the width.
263 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1052 = 4 × width
To find the value of width, we need to shift 4 to the left side.
1052/4 = width
Width = 263.
Problem 3
There are 526 boxes and 1052 candies. How many candies will be in each box?
Each box will have 2 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
1052/526 = 2
Problem 4
In a factory, there are 1052 workers, and 263 teams. How many workers are there in each team?
There are 4 workers in each team.
Explanation
Dividing the workers by the total teams, we will get the number of workers in each team.
1052/263 = 4
Problem 5
1052 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has 263 books.
Explanation
Divide total books with shelves.
1052/4 = 263
FAQs on Factors of 1052
1.What are the factors of 1052?
2.Mention the prime factors of 1052.
3.Is 1052 a multiple of 4?
4.Mention the factor pairs of 1052?
5.What is the square of 1052?
Important Glossaries for Factor of 1052
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1052 are 1, 2, 4, 263, 526, and 1052.
- Prime factors: The factors which are prime numbers. For example, 2 and 263 are prime factors of 1052.
- 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 1052 are (1, 1052), (2, 526), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, 1052 = 2² × 263.
- Multiple: A number that can be divided by another number without a remainder. For example, 1052 is a multiple of 4.
Explore More numbers
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.
