126 LearnersLast updated on May 26th, 2025
Factors of 1040
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 1040, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1040?
The numbers that divide 1040 evenly are known as factors of 1040.
A factor of 1040 is a number that divides the number without remainder.
The factors of 1040 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 65, 80, 104, 130, 160, 208, 260, 520, and 1040.
Negative factors of 1040: -1, -2, -4, -5, -8, -10, -13, -16, -20, -26, -32, -40, -52, -65, -80, -104, -130, -160, -208, -260, -520, and -1040.
Prime factors of 1040: 2, 5, and 13.
Prime factorization of 1040: 24 × 5 × 13.
The sum of factors of 1040: 1 + 2 + 4 + 5 + 8 + 10 + 13 + 16 + 20 + 26 + 32 + 40 + 52 + 65 + 80 + 104 + 130 + 160 + 208 + 260 + 520 + 1040 = 3120
How to Find Factors of 1040?
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 1040. Identifying the numbers which are multiplied to get the number 1040 is the multiplication method.
Step 1: Multiply 1040 by 1, 1040 × 1 = 1040.
Step 2: Check for other numbers that give 1040 after multiplying
2 × 520 = 1040
4 × 260 = 1040
5 × 208 = 1040
8 × 130 = 1040
10 × 104 = 1040
13 × 80 = 1040
16 × 65 = 1040
20 × 52 = 1040
26 × 40 = 1040
32 × 32.5 = 1040 (not a whole number pair)
Therefore, the positive factor pairs of 1040 are: (1, 1040), (2, 520), (4, 260), (5, 208), (8, 130), (10, 104), (13, 80), (16, 65), (20, 52), (26, 40). 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 results as a whole numbers as factors. Factors can be calculated by following simple division method -
Step 1: Divide 1040 by 1, 1040 ÷ 1 = 1040.
Step 2: Continue dividing 1040 by the numbers until the remainder becomes 0.
1040 ÷ 1 = 1040
1040 ÷ 2 = 520
1040 ÷ 4 = 260
1040 ÷ 5 = 208
1040 ÷ 8 = 130
1040 ÷ 10 = 104
1040 ÷ 13 = 80
1040 ÷ 16 = 65
1040 ÷ 20 = 52
1040 ÷ 26 = 40
Therefore, the factors of 1040 are: 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 65, 80, 104, 130, 160, 208, 260, 520, 1040.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1040 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1040 ÷ 2 = 520
520 ÷ 2 = 260
260 ÷ 2 = 130
130 ÷ 2 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 1040 are 2, 5, and 13.
The prime factorization of 1040 is: 24 × 5 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1040 is divided by 2 to get 520.
Step 2: Now divide 520 by 2 to get 260.
Step 3: Then divide 260 by 2 to get 130.
Step 4: Divide 130 by 2 to get 65.
Step 5: Divide 65 by 5 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1040 is: 24 × 5 × 13.
Factor Pairs: Two numbers that are multiplied to give a specific number are called as factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1040: (1, 1040), (2, 520), (4, 260), (5, 208), (8, 130), (10, 104), (13, 80), (16, 65), (20, 52), (26, 40).
Negative factor pairs of 1040: (-1, -1040), (-2, -520), (-4, -260), (-5, -208), (-8, -130), (-10, -104), (-13, -80), (-16, -65), (-20, -52), (-26, -40).
Common Mistakes and How to Avoid Them in Factors of 1040
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 1040, 1 and 1040 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 1040 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 32.5 as a factor, because 1040/32.5 = 32, 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 1040 are prime numbers. For example, 2, 5, and 13 are the prime factors of 1040, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1040 as 2^4 × 5 × 13 and missing all the key factors.
Factors of 1040 Examples
Problem 1
There are 13 friends and 1040 apples. How will they divide it equally?
They will get 80 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of friends.
1040/13 = 80
Problem 2
A field is rectangular, the length of the field is 26 meters, and the total area is 1040 square meters. Find the width?
40 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1040 = 26 × width
To find the value of width, we need to shift 26 to the left side.
1040/26 = width
Width = 40.
Problem 3
There are 20 bags and 1040 candies. How many candies will be in each bag?
Each bag will have 52 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
1040/20 = 52
Problem 4
In a class, there are 1040 students, and 16 groups. How many students are there in each group?
There are 65 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1040/16 = 65
Problem 5
1040 books need to be arranged in 10 shelves. How many books will go on each shelf?
Each of the shelves has 104 books.
Explanation
Divide total books with shelves.
1040/10 = 104
FAQs on Factors of 1040
1.What are the factors of 1040?
2.Mention the prime factors of 1040.
3.Is 1040 a multiple of 8?
4.Mention the factor pairs of 1040?
5.What is the square of 1040?
Important Glossaries for Factor of 1040
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1040 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 65, 80, 104, 130, 160, 208, 260, 520, and 1040.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 1040.
- 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 1040 are (1, 1040), (2, 520), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1040 is 24 × 5 × 13.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to the given number. For example, using the multiplication method to find factor pairs of 1040 like (2, 520).
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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.
