125 LearnersLast updated on May 26th, 2025
Factors of 696
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 696, how they are used in real life, and tips to learn them quickly.
What are the Factors of 696?
The numbers that divide 696 evenly are known as factors of 696.
A factor of 696 is a number that divides the number without remainder.
The factors of 696 are 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, and 696.
Negative factors of 696: -1, -2, -3, -4, -6, -8, -12, -24, -29, -58, -87, -116, -174, -232, -348, and -696.
Prime factors of 696: 2, 3, and 29.
Prime factorization of 696: 2³ × 3 × 29.
The sum of factors of 696: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 29 + 58 + 87 + 116 + 174 + 232 + 348 + 696 = 1800.
How to Find Factors of 696?
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 696. Identifying the numbers which are multiplied to get the number 696 is the multiplication method.
Step 1: Multiply 696 by 1, 696 × 1 = 696.
Step 2: Check for other numbers that give 696 after multiplying
2 × 348 = 696
3 × 232 = 696
4 × 174 = 696
6 × 116 = 696
8 × 87 = 696
12 × 58 = 696
24 × 29 = 696
Therefore, the positive factor pairs of 696 are: (1, 696), (2, 348), (3, 232), (4, 174), (6, 116), (8, 87), (12, 58), and (24, 29).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 696 by 1, 696 ÷ 1 = 696.
Step 2: Continue dividing 696 by the numbers until the remainder becomes 0.
696 ÷ 1 = 696
696 ÷ 2 = 348
696 ÷ 3 = 232
696 ÷ 4 = 174
696 ÷ 6 = 116
696 ÷ 8 = 87
696 ÷ 12 = 58
696 ÷ 24 = 29
Therefore, the factors of 696 are: 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696.
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 696 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
696 ÷ 2 = 348
348 ÷ 2 = 174
174 ÷ 2 = 87
87 ÷ 3 = 29
29 ÷ 29 = 1
The prime factors of 696 are 2, 3, and 29.
The prime factorization of 696 is: 2³ × 3 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 696 is divided by 2 to get 348.
Step 2: Now divide 348 by 2 to get 174.
Step 3: Then divide 174 by 2 to get 87.
Step 4: Divide 87 by 3 to get 29. Here, 29 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 696 is: 2³ × 3 × 29.
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 696: (1, 696), (2, 348), (3, 232), (4, 174), (6, 116), (8, 87), (12, 58), and (24, 29).
Negative factor pairs of 696: (-1, -696), (-2, -348), (-3, -232), (-4, -174), (-6, -116), (-8, -87), (-12, -58), and (-24, -29).
Common Mistakes and How to Avoid Them in Factors of 696
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 word. Always remember to include 1 and the number itself.
For example, in factors of 696, 1 and 696 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 696 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 696/1.5 = 464, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 696 are prime numbers.
For example, 2, 3, and 29 are the prime factors of 696, but it has other factors like 4, 58.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 696 as 2³ × 3 × 29 and missing all the key factors.
Factors of 696 Examples
Problem 1
There are 6 teams and 696 points in a game. How will they divide it equally?
Each team will get 116 points.
Explanation
To divide the points equally, we need to divide the total points with the number of teams.
696/6 = 116
Problem 2
A rectangular garden has a length of 24 meters and a total area of 696 square meters. Find the width.
29 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
696 = 24 × width
To find the value of width, we need to shift 24 to the left side.
696/24 = width
Width = 29.
Problem 3
There are 12 boxes and 696 marbles. How many marbles will be in each box?
Each box will have 58 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
696/12 = 58
Problem 4
In a theater, there are 696 seats divided into 29 rows. How many seats are there in each row?
There are 24 seats in each row.
Explanation
Dividing the seats with the total rows, we will get the number of seats in each row.
696/29 = 24
Problem 5
696 apples need to be distributed across 87 baskets. How many apples will go in each basket?
Each of the baskets will have 8 apples.
Explanation
Divide total apples with baskets.
696/87 = 8
FAQs on Factors of 696
1.What are the factors of 696?
2.Mention the prime factors of 696.
3.Is 696 a multiple of 12?
4.Mention the factor pairs of 696?
5.What is the square of 696?
Important Glossaries for Factor of 696
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 696 are 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, and 696.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 29 are prime factors of 696.
- 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 696 are (1, 696), (2, 348), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 696 is 2³ × 3 × 29.
- Multiple: A number that can be divided by another number without a remainder. For example, 696 is a multiple of 12.
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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.
