113 LearnersLast updated on May 26th, 2025
Factors of 1038
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 1038, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1038?
The numbers that divide 1038 evenly are known as factors of 1038.
A factor of 1038 is a number that divides the number without remainder.
The factors of 1038 are 1, 2, 3, 6, 173, 346, 519, and 1038.
Negative factors of 1038: -1, -2, -3, -6, -173, -346, -519, and -1038.
Prime factors of 1038: 2, 3, and 173.
Prime factorization of 1038: 2 × 3 × 173.
The sum of factors of 1038: 1 + 2 + 3 + 6 + 173 + 346 + 519 + 1038 = 2088
How to Find Factors of 1038?
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 1038. Identifying the numbers which are multiplied to get the number 1038 is the multiplication method.
Step 1: Multiply 1038 by 1, 1038 × 1 = 1038.
Step 2: Check for other numbers that give 1038 after multiplying
2 × 519 = 1038
3 × 346 = 1038
6 × 173 = 1038
Therefore, the positive factor pairs of 1038 are: (1, 1038), (2, 519), (3, 346), (6, 173). All these factor pairs result in 1038. 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 1038 by 1, 1038 ÷ 1 = 1038.
Step 2: Continue dividing 1038 by the numbers until the remainder becomes 0.
1038 ÷ 1 = 1038
1038 ÷ 2 = 519
1038 ÷ 3 = 346
1038 ÷ 6 = 173
Therefore, the factors of 1038 are: 1, 2, 3, 6, 173, 346, 519, 1038.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 1038 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1038 ÷ 2 = 519
519 ÷ 3 = 173
173 ÷ 173 = 1
The prime factors of 1038 are 2, 3, and 173.
The prime factorization of 1038 is: 2 × 3 × 173.
Factor Tree
The factor tree is a graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1038 is divided by 2 to get 519.
Step 2: Now divide 519 by 3 to get 173.
Step 3: 173 is a prime number and cannot be divided anymore.
So, the prime factorization of 1038 is: 2 × 3 × 173.
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 1038: (1, 1038), (2, 519), (3, 346), and (6, 173).
Negative factor pairs of 1038: (-1, -1038), (-2, -519), (-3, -346), and (-6, -173).
Common Mistakes and How to Avoid Them in Factors of 1038
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 1038, 1 and 1038 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 1038 consist of -1, -2, -3, 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 1038/1.5 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 1038 are prime numbers.
For example, 2, 3, and 173 are the prime factors of 1038, but it has other factors like 6, 346.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1038 as 2 × 3 × 173 and missing all the key factors.
Factors of 1038 Examples
Problem 1
A baker has 1038 cupcakes and wants to arrange them in boxes of 6. How many complete boxes can be made?
173 complete boxes can be made.
Explanation
To determine the number of complete boxes, divide the total cupcakes by the number per box. 1038/6 = 173
Problem 2
A gardener has a triangular patch with a total area of 1038 square meters and a base of 346 meters. What is the height of the triangle?
6 meters.
Explanation
To find the height, use the formula for the area of a triangle: Area = 0.5 × base × height 1038 = 0.5 × 346 × height To find the value of height, rearrange the formula: 1038/(0.5 × 346) = height Height = 6
Problem 3
There are 173 gift bags, and each needs an identical set of 1038 stickers. How many stickers are in each set?
Each set has 6 stickers.
Explanation
To find the number of stickers in each set, divide the total stickers by the number of bags. 1038/173 = 6
Problem 4
A charity has 519 blankets and wants to distribute them equally among 3 shelters. How many blankets does each shelter receive?
Each shelter receives 173 blankets.
Explanation
Divide the total number of blankets by the number of shelters to find the number each shelter receives. 519/3 = 173
Problem 5
A farmer grows 1038 kilograms of apples and wants to pack them in crates of 2 kilograms each. How many crates will be needed?
519 crates will be needed.
Explanation
Divide the total kilograms of apples by the weight per crate. 1038/2 = 519
FAQs on Factors of 1038
1.What are the factors of 1038?
2.Mention the prime factors of 1038.
3.Is 1038 a multiple of 3?
4.Mention the factor pairs of 1038?
5.What is the square of 1038?
6.How can children in United States use numbers in everyday life to understand Factors of 1038?
7.What are some fun ways kids in United States can practice Factors of 1038 with numbers?
8.What role do numbers and Factors of 1038 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 1038 skills?
Important Glossaries for Factor of 1038
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1038 are 1, 2, 3, 6, 173, 346, 519, and 1038.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 173 are prime factors of 1038.
- 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 1038 are (1, 1038), (2, 519), etc.
- Prime factorization: Breaking down a composite number into a product of its prime factors. For example, the prime factorization of 1038 is 2 × 3 × 173.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the number. For example, using 2 × 519 to find factors of 1038.
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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.
