102 LearnersLast updated on May 26th, 2025
Factors of 1696
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 1696, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1696?
The numbers that divide 1696 evenly are known as factors of 1696.
A factor of 1696 is a number that divides the number without remainder.
The factors of 1696 are 1, 2, 4, 8, 16, 53, 106, 212, 424, 848, and 1696.
Negative factors of 1696: -1, -2, -4, -8, -16, -53, -106, -212, -424, -848, and -1696.
Prime factors of 1696: 2 and 53.
Prime factorization of 1696: 24 × 53.
The sum of factors of 1696: 1 + 2 + 4 + 8 + 16 + 53 + 106 + 212 + 424 + 848 + 1696 = 3370
How to Find Factors of 1696?
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 1696. Identifying the numbers which are multiplied to get the number 1696 is the multiplication method.
Step 1: Multiply 1696 by 1, 1696 × 1 = 1696.
Step 2: Check for other numbers that give 1696 after multiplying
2 × 848 = 1696
4 × 424 = 1696
8 × 212 = 1696
16 × 106 = 1696
53 × 32 = 1696
Therefore, the positive factor pairs of 1696 are: (1, 1696), (2, 848), (4, 424), (8, 212), (16, 106), (53, 32).
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 the simple division method
Step 1: Divide 1696 by 1, 1696 ÷ 1 = 1696.
Step 2: Continue dividing 1696 by the numbers until the remainder becomes 0.
1696 ÷ 1 = 1696
1696 ÷ 2 = 848
1696 ÷ 4 = 424
1696 ÷ 8 = 212
1696 ÷ 16 = 106
1696 ÷ 53 = 32
Therefore, the factors of 1696 are: 1, 2, 4, 8, 16, 53, 106, 212, 424, 848, 1696.
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 1696 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1696 ÷ 2 = 848
848 ÷ 2 = 424
424 ÷ 2 = 212
212 ÷ 2 = 106
106 ÷ 53 = 2
2 ÷ 2 = 1
The prime factors of 1696 are 2 and 53.
The prime factorization of 1696 is: 24 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1696 is divided by 2 to get 848.
Step 2: Now divide 848 by 2 to get 424.
Step 3: Then divide 424 by 2 to get 212.
Step 4: Divide 212 by 2 to get 106.
Step 5: Divide 106 by 53 to get 2. Here, 2 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1696 is: 24 × 53.
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 1696: (1, 1696), (2, 848), (4, 424), (8, 212), (16, 106), and (53, 32).
Negative factor pairs of 1696: (-1, -1696), (-2, -848), (-4, -424), (-8, -212), (-16, -106), and (-53, -32).
Common Mistakes and How to Avoid Them in Factors of 1696
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 1696, 1 and 1696 are also factors.
Factors of 1696 Examples
Problem 1
There are 16 teams and 1696 medals. How will they divide it equally?
They will get 106 medals each.
Explanation
To divide the medals equally, we need to divide the total medals with the number of teams.
1696/16 = 106
Problem 2
A garden is rectangular, the length of the garden is 53 meters and the total area is 1696 square meters. Find the width?
32 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1696 = 53 × width
To find the value of width, we need to shift 53 to the left side.
1696/53 = width
Width = 32.
Problem 3
There are 8 containers and 1696 liters of water. How much water will be in each container?
Each container will have 212 liters.
Explanation
To find the water in each container, divide the total liters with the containers.
1696/8 = 212
Problem 4
In a camp, there are 424 people, and 2 groups. How many people are there in each group?
There are 212 people in each group.
Explanation
Dividing the people with the total groups, we will get the number of people in each group.
424/2 = 212
Problem 5
1696 books need to be arranged in 53 shelves. How many books will go on each shelf?
Each of the shelves has 32 books.
Explanation
Divide total books with shelves.
1696/53 = 32
FAQs on Factors of 1696
1.What are the factors of 1696?
2.Mention the prime factors of 1696.
3.Is 1696 a multiple of 4?
4.Mention the factor pairs of 1696?
5.What is the square of 1696?
Important Glossaries for Factors of 1696
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1696 are 1, 2, 4, 8, 16, 53, 106, 212, 424, 848, and 1696.
- Prime factors: The factors which are prime numbers. For example, 2 and 53 are prime factors of 1696.
- 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 1696 are (1, 1696), (2, 848), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1696 is 24 × 53.
- Multiplication method: Finding factors by identifying pairs of numbers that multiply to the original number. For example, using multiplication to find factors of 1696.
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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.
