132 LearnersLast updated on May 26th, 2025
Factors of 1105
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 1105, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1105?
The numbers that divide 1105 evenly are known as factors of 1105.
A factor of 1105 is a number that divides the number without a remainder.
The factors of 1105 are 1, 5, 13, 17, 65, 85, 221, and 1105.
Negative factors of 1105: -1, -5, -13, -17, -65, -85, -221, and -1105.
Prime factors of 1105: 5, 13, and 17.
Prime factorization of 1105: 5 × 13 × 17.
The sum of factors of 1105: 1 + 5 + 13 + 17 + 65 + 85 + 221 + 1105 = 1512
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How to Find Factors of 1105?
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 1105. Identifying the numbers that are multiplied to get the number 1105 is the multiplication method.
Step 1: Multiply 1105 by 1, 1105 × 1 = 1105.
Step 2: Check for other numbers that give 1105 after multiplying
5 × 221 = 1105
13 × 85 = 1105
17 × 65 = 1105
Therefore, the positive factor pairs of 1105 are: (1, 1105), (5, 221), (13, 85), (17, 65).
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 in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 1105 by 1, 1105 ÷ 1 = 1105.
Step 2: Continue dividing 1105 by the numbers until the remainder becomes 0.
1105 ÷ 1 = 1105
1105 ÷ 5 = 221
1105 ÷ 13 = 85
1105 ÷ 17 = 65
Therefore, the factors of 1105 are: 1, 5, 13, 17, 65, 85, 221, 1105.
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 1105 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1105 ÷ 5 = 221
221 ÷ 13 = 17
17 ÷ 17 = 1
The prime factors of 1105 are 5, 13, and 17.
The prime factorization of 1105 is: 5 × 13 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1105 is divided by 5 to get 221.
Step 2: Now divide 221 by 13 to get 17.
Step 3: Divide 17 by 17 to get 1. Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1105 is: 5 × 13 × 17.
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 1105: (1, 1105), (5, 221), (13, 85), (17, 65).
Negative factor pairs of 1105: (-1, -1105), (-5, -221), (-13, -85), (-17, -65).
Common Mistakes and How to Avoid Them in Factors of 1105
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
People 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 1105, 1 and 1105 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1105 include -1, -5, -13, etc.
Mistake 3
Including the Fraction
People might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 1105/1.5 = 736.666, 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 1105 are prime numbers.
For example, 5, 13, and 17 are the prime factors of 1105, but it has other factors like 65, 85.
Mistake 5
Mistake in Factorization
Mistakes might occur when skipping steps in factorization and writing wrong factors.
For example, not breaking 1105 as 5 × 13 × 17 and missing all the key factors.
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Factors of 1105 Examples
Problem 1
There are 5 teams and 1105 points. How will they divide it equally?
Each team will get 221 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
1105/5 = 221
Problem 2
A garden is rectangular, the length of the garden is 17 meters and the total area is 1105 square meters. Find the width.
65 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 1105 = 17 × width
To find the value of width, we need to shift 17 to the left side.
1105/17 = width
Width = 65.
Problem 3
There are 13 boxes and 1105 apples. How many apples will be in each box?
Each box will have 85 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
1105/13 = 85
Problem 4
In a club, there are 1105 members, and 17 sections. How many members are there in each section?
There are 65 members in each section.
Explanation
Dividing the members by the total sections, we will get the number of members in each section.
1105/17 = 65
Problem 5
1105 books need to be arranged in 221 shelves. How many books will go on each shelf?
Each of the shelves has 5 books.
Explanation
Divide total books by shelves.
1105/221 = 5
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FAQs on Factors of 1105
1.What are the factors of 1105?
2.Mention the prime factors of 1105.
3.Is 1105, a multiple of 13?
4.Mention the factor pairs of 1105?
5.What is the square of 1105?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1105?
7.What are some fun ways kids in Qatar can practice Factors of 1105 with numbers?
8.What role do numbers and Factors of 1105 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1105 skills?
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Important Glossaries for Factors of 1105
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1105 are 1, 5, 13, 17, 65, 85, 221, and 1105.
- Prime factors: The factors which are prime numbers. For example, 5, 13, and 17 are prime factors of 1105.
- 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 1105 are (1, 1105), (5, 221), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, 1105 is 5 × 13 × 17.
- Divisibility: The ability of one number to be divided by another without a remainder. For example, 1105 is divisible by 5.
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About BrightChamps in Qatar
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.
