117 LearnersLast updated on May 26th, 2025
Factors of 1045
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 1045, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1045?
The numbers that divide 1045 evenly are known as factors of 1045.
A factor of 1045 is a number that divides the number without remainder.
The factors of 1045 are 1, 5, 209, and 1045
Negative factors of 1045: -1, -5, -209, and -1045.
Prime factors of 1045: 5 and 209.
Prime factorization of 1045: 5 × 11 × 19.
The sum of factors of 1045: 1 + 5 + 209 + 1045 = 1260
How to Find Factors of 1045?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1045. Identifying the numbers which are multiplied to get the number 1045 is the multiplication method.
Step 1: Multiply 1045 by 1, 1045 × 1 = 1045.
Step 2: Check for other numbers that give 1045 after multiplying
5 × 209 = 1045
Therefore, the positive factor pairs of 1045 are: (1, 1045) and (5, 209). All these factor pairs result in 1045. 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 1045 by 1, 1045 ÷ 1 = 1045.
Step 2: Continue dividing 1045 by the numbers until the remainder becomes 0.
1045 ÷ 1 = 1045
1045 ÷ 5 = 209
Therefore, the factors of 1045 are: 1, 5, 209, 1045.
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 1045 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1045 ÷ 5 = 209
209 ÷ 11 = 19
19 ÷ 19 = 1
The prime factors of 1045 are 5, 11, and 19.
The prime factorization of 1045 is: 5 × 11 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1045 is divided by 5 to get 209.
Step 2: Now divide 209 by 11 to get 19.
Step 3: 19 is the smallest prime number, which cannot be divided anymore.
So, the prime factorization of 1045 is: 5 × 11 × 19.
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 1045: (1, 1045) and (5, 209).
Negative factor pairs of 1045: (-1, -1045) and (-5, -209).
Common Mistakes and How to Avoid Them in Factors of 1045
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 1045, 1 and 1045 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 1045 consist of -1, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes mistakenly add fractions as factors. Only whole numbers can be factors.
For example, thinking 2.5 is a factor because 1045/2.5 = 418, but 418 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 1045 are prime numbers.
For example, 5, 11, and 19 are the prime factors of 1045, but it has other factors like 209, 1045.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1045 as 5 × 11 × 19 and missing all the key factors.
Factors of 1045 Examples
Problem 1
A farmer has 1045 apples and sells them in packs of 5. How many full packs can the farmer make?
The farmer can make 209 full packs.
Explanation
To find the number of full packs, divide the total number of apples by the number in each pack.
1045/5 = 209
Problem 2
A rectangular field has a length of 5 meters and a total area of 1045 square meters. Find the width.
209 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1045 = 5 × width
To find the value of width, we need to shift 5 to the left side.
1045/5 = width
Width = 209.
Problem 3
A teacher has 1045 pencils and wants to distribute them equally among 11 students. How many pencils will each student get?
Each student will get 95 pencils.
Explanation
To find the number of pencils each student gets, divide the total number of pencils by the number of students.
1045/11 = 95
Problem 4
A company has 1045 units of a product and packs them into boxes of 19 units each. How many boxes can be filled?
55 boxes can be filled.
Explanation
Divide the total number of units by the number of units per box.
1045/19 = 55
Problem 5
A library has 1045 books and wants to place them equally on 5 shelves. How many books will each shelf hold?
Each shelf will hold 209 books.
Explanation
Divide the total number of books by the number of shelves.
1045/5 = 209
FAQs on Factors of 1045
1.What are the factors of 1045?
2.Mention the prime factors of 1045.
3.Is 1045 a multiple of 5?
4.Mention the factor pairs of 1045?
5.What is the square of 1045?
Important Glossaries for Factors of 1045
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1045 are 1, 5, 209, and 1045.
- Prime factors: The factors which are prime numbers. For example, 5, 11, and 19 are prime factors of 1045.
- 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 1045 are (1, 1045) and (5, 209).
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1045 is 5 × 11 × 19
- Multiples: The result of multiplying a number by an integer. For example, 1045 is a multiple of 5.
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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.
