123 LearnersLast updated on May 26th, 2025
Factors of 1048
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 1048, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1048?
The numbers that divide 1048 evenly are known as factors of 1048.
A factor of 1048 is a number that divides the number without remainder.
The factors of 1048 are 1, 2, 4, 8, 131, 262, 524, and 1048.
Negative factors of 1048: -1, -2, -4, -8, -131, -262, -524, and -1048.
Prime factors of 1048: 2 and 131.
Prime factorization of 1048: 23 × 131.
The sum of factors of 1048: 1 + 2 + 4 + 8 + 131 + 262 + 524 + 1048 = 1980
How to Find Factors of 1048?
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 1048. Identifying the numbers which are multiplied to get the number 1048 is the multiplication method.
Step 1: Multiply 1048 by 1, 1048 × 1 = 1048.
Step 2: Check for other numbers that give 1048 after multiplying
2 × 524 = 1048
4 × 262 = 1048
8 × 131 = 1048
Therefore, the positive factor pairs of 1048 are: (1, 1048), (2, 524), (4, 262), (8, 131). All these factor pairs result in 1048. 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 1048 by 1, 1048 ÷ 1 = 1048.
Step 2: Continue dividing 1048 by the numbers until the remainder becomes 0.
1048 ÷ 1 = 1048
1048 ÷ 2 = 524
1048 ÷ 4 = 262
1048 ÷ 8 = 131
Therefore, the factors of 1048 are: 1, 2, 4, 8, 131, 262, 524, 1048.
Prime Factors and Prime Factorization
The factors can be found by dividing them with a prime number. 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 1048 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1048 ÷ 2 = 524
524 ÷ 2 = 262
262 ÷ 2 = 131
131 ÷ 131 = 1
The prime factors of 1048 are 2 and 131.
The prime factorization of 1048 is: 23 × 131.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1048 is divided by 2 to get 524.
Step 2: Now divide 524 by 2 to get 262.
Step 3: Then divide 262 by 2 to get 131
Step 4: Divide 131 by 131 to get 1. Here, 131 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1048 is: 23 × 131.
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 1048: (1, 1048), (2, 524), (4, 262), (8, 131).
Negative factor pairs of 1048: (-1, -1048), (-2, -524), (-4, -262), (-8, -131).
Common Mistakes and How to Avoid Them in Factors of 1048
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1048, 1 and 1048 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 1048 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1048/1.5 = 698.666..., 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 1048 are prime numbers. For example, 2 and 131 are the prime factors of 1048, but it has other factors like 4, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1048 as 2^3 × 131 and missing all the key factors.
Factors of 1048 Examples
Problem 1
There are 8 teams and 1048 points to distribute equally. How many points will each team receive?
Each team will receive 131 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
1048/8 = 131
Problem 2
A garden is rectangular, the length of the garden is 262 meters and the total area is 1048 square meters. Find the width?
4 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1048 = 262 × width
To find the value of width, we need to shift 262 to the left side.
1048/262 = width
Width = 4.
Problem 3
There are 524 packages and 1048 items. How many items will be in each package?
Each package will have 2 items.
Explanation
To find the items in each package, divide the total items by the number of packages.
1048/524 = 2
Problem 4
In a seminar, there are 1048 participants, and they are divided into 4 groups. How many participants are there in each group?
There are 262 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
1048/4 = 262
Problem 5
1048 books need to be arranged on 131 shelves. How many books will go on each shelf?
Each of the shelves has 8 books.
Explanation
Divide total books by the number of shelves.
1048/131 = 8
FAQs on Factors of 1048
1.What are the factors of 1048?
2.Mention the prime factors of 1048.
3.Is 1048 a multiple of 4?
4.Mention the factor pairs of 1048?
5.What is the square of 1048?
Important Glossaries for Factor of 1048
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1048 are 1, 2, 4, 8, 131, 262, 524, and 1048.
- Prime factors: The factors which are prime numbers. For example, 2 and 131 are prime factors of 1048.
- 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 1048 are (1, 1048), (2, 524), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1048 is 23 × 131.
- Multiplicative identity: The number 1 is the multiplicative identity because any number multiplied by 1 remains unchanged. For example, 1048 × 1 = 1048.
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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.
