100 LearnersLast updated on May 26th, 2025
Factors of 1688
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 1688, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1688?
The numbers that divide 1688 evenly are known as factors of 1688.
A factor of 1688 is a number that divides the number without remainder.
The factors of 1688 are 1, 2, 4, 8, 211, 422, 844, and 1688.
Negative factors of 1688: -1, -2, -4, -8, -211, -422, -844, and -1688.
Prime factors of 1688: 2 and 211.
Prime factorization of 1688: 23 × 211.
The sum of factors of 1688: 1 + 2 + 4 + 8 + 211 + 422 + 844 + 1688 = 3180
How to Find Factors of 1688?
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 1688. Identifying the numbers which are multiplied to get the number 1688 is the multiplication method.
Step 1: Multiply 1688 by 1, 1688 × 1 = 1688.
Step 2: Check for other numbers that give 1688 after multiplying
2 × 844 = 1688
4 × 422 = 1688
8 × 211 = 1688
Therefore, the positive factor pairs of 1688 are: (1, 1688), (2, 844), (4, 422), (8, 211).
All these factor pairs result in 1688.
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 which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1688 by 1, 1688 ÷ 1 = 1688.
Step 2: Continue dividing 1688 by the numbers until the remainder becomes 0.
1688 ÷ 1 = 1688
1688 ÷ 2 = 844
1688 ÷ 4 = 422
1688 ÷ 8 = 211
Therefore, the factors of 1688 are: 1, 2, 4, 8, 211, 422, 844, 1688.
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 1688 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1688 ÷ 2 = 844
844 ÷ 2 = 422
422 ÷ 2 = 211
211 ÷ 211 = 1
The prime factors of 1688 are 2 and 211.
The prime factorization of 1688 is: 23 × 211.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 1688 is divided by 2 to get 844.
Step 2: Now divide 844 by 2 to get 422.
Step 3: Then divide 422 by 2 to get 211. Here, 211 is a prime number that cannot be divided anymore. So, the prime factorization of 1688 is: 23 × 211.
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 1688: (1, 1688), (2, 844), (4, 422), and (8, 211).
Negative factor pairs of 1688: (-1, -1688), (-2, -844), (-4, -422), and (-8, -211).
Common Mistakes and How to Avoid Them in Factors of 1688
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1688, 1 and 1688 are also factors.
Factors of 1688 Examples
Problem 1
There are 8 friends and 1688 candies. How will they divide it equally?
They will get 211 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1688/8 = 211
Problem 2
A field is rectangular, the length of the field is 211 meters and the total area is 1688 square meters. Find the width?
8 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1688 = 211 × width
To find the value of width, we need to shift 211 to the left side.
1688/211 = width
Width = 8.
Problem 3
There are 4 baskets and 1688 apples. How many apples will be in each basket?
Each basket will have 422 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1688/4 = 422
Problem 4
In a conference, there are 1688 participants and 211 tables. How many participants are there at each table?
There are 8 participants at each table.
Explanation
Dividing the participants by the total tables, we will get the number of participants at each table.
1688/211 = 8
Problem 5
1688 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 844 books.
Explanation
Divide total books by shelves.
1688/2 = 844
FAQs on Factors of 1688
1.What are the factors of 1688?
2.Mention the prime factors of 1688.
3.Is 1688 a multiple of 4?
4.Mention the factor pairs of 1688?
5.What is the square of 1688?
Important Glossaries for Factor of 1688
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1688 are 1, 2, 4, 8, 211, 422, 844, and 1688.
- Prime factors: The factors which are prime numbers. For example, 2 and 211 are prime factors of 1688.
- 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 1688 are (1, 1688), (2, 844), etc.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 1688 is a multiple of 4.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1688 is 2^3 × 211.
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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.
