119 LearnersLast updated on May 26th, 2025
Factors of -196
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 -196, how they are used in real life, and tips to learn them quickly.
What are the Factors of -196?
The numbers that divide -196 evenly are known as factors of -196.
A factor of -196 is a number that divides the number without remainder.
The factors of -196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
Negative factors of -196: -1, -2, -4, -7, -14, -28, -49, -98, and -196.
Prime factors of 196: 2 and 7. Prime factorization of 196: (22 times 72).
The sum of factors of 196: 1 + 2 + 4 + 7 + 14 + 28 + 49 + 98 + 196 = 399
How to Find Factors of -196?
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 196. Identifying the numbers which are multiplied to get the number 196 is the multiplication method.
Step 1: Multiply 196 by 1, 196 × 1 = 196.
Step 2: Check for other numbers that give 196 after multiplying 2 × 98 = 196 4 × 49 = 196 7 × 28 = 196
Therefore, the positive factor pairs of 196 are: (1, 196), (2, 98), (4, 49), (7, 28).
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 196 by 1, 196 ÷ 1 = 196.
Step 2: Continue dividing 196 by the numbers until the remainder becomes 0.
196 ÷ 1 = 196
196 ÷ 2 = 98
196 ÷ 4 = 49
196 ÷ 7 = 28
Therefore, the factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, 196.
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 196 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
196 ÷ 2 = 98
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 196 are 2 and 7.
The prime factorization of 196 is: (22 times 72).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 196 is divided by 2 to get 98.
Step 2: Now divide 98 by 2 to get 49.
Step 3: Then divide 49 by 7 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 196 is: (22 times 72).
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 196: (1, 196), (2, 98), (4, 49), (7, 28).
Negative factor pairs of 196: (-1, -196), (-2, -98), (-4, -49), (-7, -28).
Common Mistakes and How to Avoid Them in Factors of -196
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 196, 1 and 196 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 -196 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 196/1.5 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 196 are prime numbers. For example, 2 and 7 are the prime factors of 196, but it has other factors like 4, 14.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 196 as \(2^2 \times 7^2\) and missing all the key factors.
Factors of -196 Examples
Problem 1
A classroom project requires 196 sheets of paper, and there are 7 students. How many sheets does each student get if distributed equally?
Each student will get 28 sheets.
Explanation
To divide the sheets equally, we need to divide the total sheets by the number of students.
196/7 = 28
Problem 2
A garden plot is rectangular, the width of the plot is 14 meters and the total area is 196 square meters. Find the length.
14 meters.
Explanation
To find the length of the plot, we use the formula,
Area = length × width
196 = length × 14
To find the value of length, we need to shift 14 to the left side.
196/14 = length
Length = 14.
Problem 3
There are 4 containers and 196 liters of water. How many liters will be in each container?
Each container will have 49 liters.
Explanation
To find the liters in each container, divide the total liters by the containers.
196/4 = 49
Problem 4
A pack contains 196 marbles, and there are 28 children. How many marbles does each child get if distributed equally?
Each child gets 7 marbles.
Explanation
Dividing the marbles by the number of children, we will get the number of marbles each child gets.
196/28 = 7
Problem 5
196 apples need to be arranged in 49 baskets. How many apples will go in each basket?
Each basket will have 4 apples.
Explanation
Divide total apples by the number of baskets.
196/49 = 4
FAQs on Factors of -196
1.What are the factors of -196?
2.Mention the prime factors of 196.
3.Is 196 a multiple of 7?
4.Mention the factor pairs of -196?
5.What is the square root of 196?
6.How can children in United States use numbers in everyday life to understand Factors of -196?
7.What are some fun ways kids in United States can practice Factors of -196 with numbers?
8.What role do numbers and Factors of -196 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of -196 skills?
Important Glossaries for Factor of -196
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
- Prime factors: The factors that are prime numbers. For example, 2 and 7 are prime factors of 196.
- 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 196 are (1, 196), (2, 98), etc.
- Negative factors: These are the negative counterparts of the positive factors. For example, -1, -2, -4, -7, etc., are negative factors of -196.
- Prime factorization: It is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 196 is \(2^2 \times 7^2\).
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About BrightChamps in United States
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.
