Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 5 teams and 1705 points to distribute. How will they distribute it equally?
They will distribute 341 points to each team.
To distribute the points equally, divide the total points by the number of teams.
1705/5 = 341
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.
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.
There are 11 boxes and 1705 marbles. How many marbles will be in each box?
Each box will have 155 marbles.
To find the marbles in each box, divide the total marbles by the number of boxes.
1705/11 = 155
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.
Dividing the participants by the total groups, we will get the number of participants in each group.
1705/31 = 55
1705 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 341 books.
Divide total books by shelves.
1705/5 = 341
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.
: She loves to read number jokes and games.