101 LearnersLast updated on May 26th, 2025
Factors of 1690
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 1690, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1690?
The numbers that divide 1690 evenly are known as factors of 1690.
A factor of 1690 is a number that divides the number without remainder.
The factors of 1690 are 1, 2, 5, 13, 26, 65, 130, 169, 338, 845, and 1690.
Negative factors of 1690: -1, -2, -5, -13, -26, -65, -130, -169, -338, -845, and -1690.
Prime factors of 1690: 2, 5, and 13.
Prime factorization of 1690: 2 × 5 × 13 × 13.
The sum of factors of 1690: 1 + 2 + 5 + 13 + 26 + 65 + 130 + 169 + 338 + 845 + 1690 = 3284
How to Find Factors of 1690?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 1690. Identifying the numbers which are multiplied to get the number 1690 is the multiplication method.
Step 1: Multiply 1690 by 1, 1690 × 1 = 1690.
Step 2: Check for other numbers that give 1690 after multiplying
2 × 845 = 1690
5 × 338 = 1690
13 × 130 = 1690
26 × 65 = 1690
Therefore, the positive factor pairs of 1690 are: (1, 1690), (2, 845), (5, 338), (13, 130), (26, 65).
All these factor pairs result in 1690.
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 as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1690 by 1, 1690 ÷ 1 = 1690.
Step 2: Continue dividing 1690 by the numbers until the remainder becomes 0.
1690 ÷ 1 = 1690
1690 ÷ 2 = 845
1690 ÷ 5 = 338
1690 ÷ 13 = 130
1690 ÷ 26 = 65
Therefore, the factors of 1690 are: 1, 2, 5, 13, 26, 65, 130, 169, 338, 845, 1690.
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 1690 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1690 ÷ 2 = 845
845 ÷ 5 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1
The prime factors of 1690 are 2, 5, and 13.
The prime factorization of 1690 is: 2 × 5 × 13 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1690 is divided by 2 to get 845.
Step 2: Now divide 845 by 5 to get 169. Step 3: Then divide 169 by 13 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1690 is: 2 × 5 × 13 × 13.
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 1690: (1, 1690), (2, 845), (5, 338), (13, 130), and (26, 65).
Negative factor pairs of 1690: (-1, -1690), (-2, -845), (-5, -338), (-13, -130), and (-26, -65).
Common Mistakes and How to Avoid Them in Factors of 1690
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 1690, 1 and 1690 is also a factor.
Factors of 1690 Examples
Problem 1
There are 13 friends and 1690 candies. How will they divide it equally?
They will get 130 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
1690/13 = 130
Problem 2
A field is rectangular, the length of the field is 26 meters and the total area is 1690 square meters. Find the width?
65 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1690 = 26 × width
To find the value of width, we need to shift 26 to the left side.
1690/26 = width
Width = 65.
Problem 3
There are 338 gift boxes and 1690 chocolates. How many chocolates will be in each box?
Each box will have 5 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates with the boxes.
1690/338 = 5
Problem 4
In a class, there are 1690 students, and 130 groups. How many students are there in each group?
There are 13 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1690/130 = 13
Problem 5
1690 books need to be arranged in 26 shelves. How many books will go on each shelf?
Each of the shelves has 65 books.
Explanation
Divide total books with shelves.
1690/26 = 65
FAQs on Factors of 1690
1.What are the factors of 1690?
2.Mention the prime factors of 1690.
3.Is 1690 a multiple of 5?
4.Mention the factor pairs of 1690?
5.What is the square of 1690?
Important Glossaries for Factor of 1690
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1690 are 1, 2, 5, 13, 26, 65, 130, 169, 338, 845, and 1690.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 1690.
- 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 1690 are (1, 1690), (2, 845), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1690 is 2 × 5 × 13 × 13.
- Negative factors: Factors that are negative. For example, -1, -2, -5, -13, -26, -65, -130, -169, -338, -845, and -1690 are negative factors of 1690.
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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.
