100 LearnersLast updated on May 26th, 2025
Factors of 1695
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 1695, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1695?
The numbers that divide 1695 evenly are known as factors of 1695.
A factor of 1695 is a number that divides the number without remainder.
The factors of 1695 are 1, 3, 5, 9, 15, 45, 113, 1695.
Negative factors of 1695: -1, -3, -5, -9, -15, -45, -113, -1695.
Prime factors of 1695: 3, 5, and 113.
Prime factorization of 1695: 3 × 5 × 113.
The sum of factors of 1695: 1 + 3 + 5 + 9 + 15 + 45 + 113 + 1695 = 1886.
How to Find Factors of 1695?
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 1695. Identifying the numbers which are multiplied to get the number 1695 is the multiplication method.
Step 1: Multiply 1695 by 1, 1695 × 1 = 1695.
Step 2: Check for other numbers that give 1695 after multiplying:
3 × 565 = 1695
5 × 339 = 1695
9 × 188 = 1695
15 × 113 = 1695
Therefore, the positive factor pairs of 1695 are: (1, 1695), (3, 565), (5, 339), (9, 188), (15, 113).
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 that result in whole numbers as factors. Factors can be calculated by following the simple division method:
Step 1: Divide 1695 by 1, 1695 ÷ 1 = 1695.
Step 2: Continue dividing 1695 by the numbers until the remainder becomes 0.
1695 ÷ 1 = 1695
1695 ÷ 3 = 565
1695 ÷ 5 = 339
1695 ÷ 9 = 188
1695 ÷ 15 = 113
Therefore, the factors of 1695 are: 1, 3, 5, 9, 15, 45, 113, 1695.
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 1695 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1695 ÷ 3 = 565
565 ÷ 5 = 113
113 ÷ 113 = 1
The prime factors of 1695 are 3, 5, and 113.
The prime factorization of 1695 is: 3 × 5 × 113.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1695 is divided by 3 to get 565.
Step 2: Now divide 565 by 5 to get 113.
Step 3: 113 is a prime number and cannot be divided further. So, the prime factorization of 1695 is: 3 × 5 × 113.
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 1695: (1, 1695), (3, 565), (5, 339), (9, 188), (15, 113).
Negative factor pairs of 1695: (-1, -1695), (-3, -565), (-5, -339), (-9, -188), (-15, -113).
Common Mistakes and How to Avoid Them in Factors of 1695
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 1695, 1 and 1695 are also factors.
Factors of 1695 Examples
Problem 1
There are 9 students and 1695 books. How will they divide the books equally?
They will get 188 books each.
Explanation
To divide the books equally, we need to divide the total books by the number of students.
1695/9 = 188
Problem 2
A plot is rectangular, the length of the plot is 15 meters and the total area is 1695 square meters. Find the width?
113 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1695 = 15 × width
To find the value of width, we need to shift 15 to the left side.
1695/15 = width
Width = 113.
Problem 3
There are 3 teams and 1695 points. How many points will each team have?
Each team will have 565 points.
Explanation
To find the points for each team, divide the total points by the teams.
1695/3 = 565
Problem 4
In a conference, there are 1695 participants, and 5 groups. How many participants are there in each group?
There are 339 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
1695/5 = 339
Problem 5
1695 gadgets need to be distributed among 15 departments. How many gadgets will go to each department?
Each department will receive 113 gadgets.
Explanation
Divide total gadgets by departments.
1695/15 = 113
FAQs on Factors of 1695
1.What are the factors of 1695?
2.Mention the prime factors of 1695.
3.Is 1695 a multiple of 3?
4.Mention the factor pairs of 1695?
5.What is the square of 1695?
Important Glossaries for Factors of 1695
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1695 are 1, 3, 5, 9, 15, 45, 113, 1695.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 113 are prime factors of 1695.
- 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 1695 are (1, 1695), (3, 565), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For 1695, it is 3 × 5 × 113.
- Multiples: The result of multiplying a number by an integer. For example, 1695 is a multiple of 3 and 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.
