120 LearnersLast updated on May 26th, 2025
Factors of 1705
Factors are the numbers that divide any given number evenly without a 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 1705, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1705?
The numbers that divide 1705 evenly are known as factors of 1705.
A factor of 1705 is a number that divides the number without a remainder.
The factors of 1705 are 1, 5, 11, 31, 55, 155, 341, and 1705.
Negative factors of 1705: -1, -5, -11, -31, -55, -155, -341, and -1705.
Prime factors of 1705: 5, 11, and 31.
Prime factorization of 1705: 5 × 11 × 31.
The sum of factors of 1705: 1 + 5 + 11 + 31 + 55 + 155 + 341 + 1705 = 2304
How to Find Factors of 1705?
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 1705. Identifying the numbers which are multiplied to get the number 1705 is the multiplication method.
Step 1: Multiply 1705 by 1, 1705 × 1 = 1705.
Step 2: Check for other numbers that give 1705 after multiplying
5 × 341 = 1705
11 × 155 = 1705
31 × 55 = 1705
Therefore, the positive factor pairs of 1705 are: (1, 1705), (5, 341), (11, 155), (31, 55).
All these factor pairs result in 1705.
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 that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1705 by 1, 1705 ÷ 1 = 1705.
Step 2: Continue dividing 1705 by the numbers until the remainder becomes 0.
1705 ÷ 1 = 1705
1705 ÷ 5 = 341
1705 ÷ 11 = 155
1705 ÷ 31 = 55
Therefore, the factors of 1705 are: 1, 5, 11, 31, 55, 155, 341, 1705.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1705 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1705 ÷ 5 = 341
341 ÷ 11 = 31
31 ÷ 31 = 1
The prime factors of 1705 are 5, 11, and 31.
The prime factorization of 1705 is: 5 × 11 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1705 is divided by 5 to get 341.
Step 2: Now divide 341 by 11 to get 31. Step 3: Here, 31 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1705 is: 5 × 11 × 31.
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 1705: (1, 1705), (5, 341), (11, 155), and (31, 55).
Negative factor pairs of 1705: (-1, -1705), (-5, -341), (-11, -155), and (-31, -55).
Common Mistakes and How to Avoid Them in Factors of 1705
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 1705, 1 and 1705 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 1705 consist of -1, -5, -11, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor because 1705/1.5 = 1136.67, 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 1705 are prime numbers.
For example, 5, 11, and 31 are the prime factors of 1705, but it has other factors like 55, 155.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1705 as 5 × 11 × 31 and missing all the key factors.
Factors of 1705 Examples
Problem 1
There are 5 teams and 1705 points to distribute. How will they distribute it equally?
They will distribute 341 points to each team.
Explanation
To distribute the points equally, divide the total points by the number of teams.
1705/5 = 341
Problem 2
A garden is rectangular, the length of the garden is 31 meters and the total area is 1705 square meters. Find the width?
55 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1705 = 31 × width
To find the value of width, shift 31 to the left side.
1705/31 = width
Width = 55.
Problem 3
There are 11 boxes and 1705 marbles. How many marbles will be in each box?
Each box will have 155 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1705/11 = 155
Problem 4
In a conference, there are 1705 participants and 31 groups. How many participants are there in each group?
There are 55 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
1705/31 = 55
Problem 5
1705 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 341 books.
Explanation
Divide total books by shelves.
1705/5 = 341
FAQs on Factors of 1705
1.What are the factors of 1705?
2.Mention the prime factors of 1705.
3.Is 1705 a multiple of 11?
4.Mention the factor pairs of 1705?
5.What is the square of 1705?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of 1705?
7.What are some fun ways kids in Saudi Arabia can practice Factors of 1705 with numbers?
8.What role do numbers and Factors of 1705 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of 1705 skills?
Important Glossaries for Factor of 1705
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1705 are 1, 5, 11, 31, 55, 155, 341, and 1705.
- Prime factors: The factors which are prime numbers. For example, 5, 11, and 31 are prime factors of 1705.
- 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 1705 are (1, 1705), (5, 341), etc.
- Multiples: A multiple of a number is the product of that number and an integer. For example, 1705 is a multiple of 5 and 11.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1705 is 5 × 11 × 31.
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About BrightChamps in Saudi Arabia
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.
