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Last updated on May 26th, 2025

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Multiples of 196

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In math, multiples are the products we get while multiplying a number with other numbers. Multiples play a key role in construction and design, counting groups of items, sharing resources equally, and managing time effectively. In this topic, we will learn the essential concepts of multiples of 196.

Multiples of 196 for Vietnamese Students
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What are the Multiples of 196?

Now, let us learn more about multiples of 196. Multiples of 196 are the numbers you get when you multiply 196 by any whole number, including zero. Each number has an infinite number of multiples, including a multiple of itself. In multiplication, a multiple of 196 can be denoted as 196 × n, where ‘n’ represents any whole number (0, 1, 2, 3,…). So, we can summarize that:

 

Multiple of a number = Number × Any whole number

 

For example, multiplying 196 × 1 will give us 196 as the product. Multiples of 196 will be larger or equal to 196.multiples of 196

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List of First 20 Multiples of 196

Multiples of 196 include the products of 196 and an integer. Multiples of 196 are divisible by 196 evenly. The first few multiples of 196 are given below:

 

TABLE OF 196 (1-10)

196 x 1 = 196

196 x 6 = 1176

196 x 2 = 392

196 x 7 = 1372

196 x 3 = 588

196 x 8 = 1568

196 x 4 = 784

196 x 9 = 1764

196 x 5 = 980

196 x 10 = 1960

 

TABLE OF 196 (11-20)

196 x 11 = 2156

196 x 16 = 3136

196 x 12 = 2352

196 x 17 = 3332

196 x 13 = 2548

196 x 18 = 3528

196 x 14 = 2744

196 x 19 = 3724

196 x 15 = 2940

196 x 20 = 3920

 

Now, we know the first few multiples of 196. They are 0, 196, 392, 588, 784, 980, 1176, 1372, 1568, 1764, 1960,..

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Operations with Multiples of 196

Understanding the multiples of 196 helps solve mathematical problems and boost our multiplication and division skills. When working with multiples of 196, we need to apply it to different mathematical operations such as addition, subtraction, multiplication, and division.

 

Sum of First 5 Multiples of 196:

 

196, 392, 588, 784, and 980 are the first five multiples of 196. When multiplying 196 from 1 to 5, we get these numbers as the products.  


So, the sum of these multiples is:


196 + 392 + 588 + 784 + 980 = 2940


When we add the first 5 multiples of 196, the answer will be 2940.

 

Subtraction of First 5 Multiples of 196:

 

While we do subtraction, it improves our comprehension of how the value decreases when each multiple is subtracted from the previous one. 196, 392, 588, 784, and 980 are the first five multiples of 196. So, let us calculate it as given below:


196 - 392 = -196  
-196 - 588 = -784  
-784 - 784 = -1568  
-1568 - 980 = -2548  


Hence, the result of subtracting the first 5 multiples of 196 is -2548.

 

Average of First 5 Multiples of 196:

 

To calculate the average, we need to identify the sum of the first 5 multiples of 196 and then divide it by the count, i.e., 5. Because there are 5 multiples presented in the calculation. Averaging helps us to understand the concepts of central tendencies and other values. We know the sum of the first 5 multiples of 196 is 2940.


196 + 392 + 588 + 784 + 980 = 2940


Next, divide the sum by 5:


2940 ÷ 5 = 588


588 is the average of the first 5 multiples of 196.

 

Product of First 5 Multiples of 196:

 

The product of given numbers is the result of multiplying all of them together. Here, the first 5 multiples of 196 include: 196, 392, 588, 784, and 980. Now, the product of these numbers is:


196 × 392 × 588 × 784 × 980 = 35,293,168,384,000


The product of the first 5 multiples of 196 is a very large number.

 

Division of First 5 Multiples of 196:

 

While we perform division, we get to know how many times 196 can fit into each of the given multiples. 196, 392, 588, 784, and 980 are the first 5 multiples of 196.


196 ÷ 196 = 1  
392 ÷ 196 = 2  
588 ÷ 196 = 3  
784 ÷ 196 = 4  
980 ÷ 196 = 5

   
The results of dividing the first 5 multiples of 196 are: 1, 2, 3, 4, and 5.

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Common Mistakes and How to Avoid Them in Multiples of 196

While working with multiples of 196, we make common mistakes. Identifying these errors and understanding how to avoid them can be helpful. Below are some frequent mistakes and tips to avoid them:

Mistake 1

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Confusing Multiples with Factors

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Sometimes, students get confused between the multiples and factors of 196. A simple trick to differentiate between the two is to remember that multiples are the products of multiplication, while factors are the divisors of the number. Multiples of 196 refer to the products we get while multiplying 196 with other numbers. For example, multiples of 196 include 0, 196, 392, 588, 784, 980, 1176,...


The factors of 196 are 1, 2, 4, 7, 14, 14, 28, 49, 98, and 196. When 196 is divided by these numbers, the remainder will be zero. These are the factors of 196 meaning that these numbers can divide 196 without any remainder.

 

Factors of 196:


196 ÷ 1 = 196  
196 ÷ 2 = 98  
196 ÷ 4 = 49  
196 ÷ 7 = 28  
196 ÷ 14 = 14  
196 ÷ 28 = 7  
196 ÷ 49 = 4  
196 ÷ 98 = 2  
196 ÷ 196 = 1  

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Multiples of 196 Examples

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Problem 1

A farmer is planting rows of trees in his orchard. Each row contains 196 trees. If he plants 5 rows this season, how many trees will be in the orchard by the end of the season?

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980 trees 

Explanation

To find the total number of trees, multiply the number of rows by the number of trees per row.

 

Number of rows = 5  
Number of trees per row = 196  

 

5 × 196 = 980  

 

Therefore, there will be 980 trees in the orchard.

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Problem 2

A factory produces toy cars in batches. Each batch contains 196 toy cars. If the factory produces 3 batches in a day, how many toy cars are produced in a week (assuming the factory operates 7 days a week)?

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4,116 toy cars 

Explanation

First, calculate the daily production, then multiply by the number of days in a week.

 

Daily production = 3 batches × 196 toy cars per batch  
= 588 toy cars per day  

 

Weekly production = 588 toy cars per day × 7 days  
= 4,116 toy cars  

 

Therefore, 4,116 toy cars are produced in a week.

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Problem 3

In a library, each shelf can hold 196 books. If the library has 10 shelves, how many books can the library hold in total?

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1,960 books

Explanation

To find the total number of books, multiply the number of shelves by the number of books each shelf can hold.

 

Number of shelves = 10  
Books per shelf = 196  

 

10 × 196 = 1,960  

 

Therefore, the library can hold 1,960 books.

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Max, the Girl Character from BrightChamps

Problem 4

A marathon is organized where each participant runs a distance of 196 meters. If there are 12 participants, what is the total distance run by all the participants combined?

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2,352 meters

Explanation

Multiply the distance run by each participant by the number of participants to find the total distance.

 

Distance per participant = 196 meters  
Number of participants = 12  

 

196 × 12 = 2,352  

 

Therefore, the total distance run by all participants is 2,352 meters.

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Max, the Girl Character from BrightChamps

Problem 5

A music festival is set up with rows of chairs for the audience. Each row contains 196 chairs. If there are 8 rows, how many chairs are available for the audience?

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1,568 chairs

Explanation

Multiply the number of rows by the number of chairs in each row to find the total number of chairs.

 

Number of rows = 8  
Chairs per row = 196  

 

8 × 196 = 1,568  

 

Therefore, there are 1,568 chairs available for the audience.

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FAQs on Multiples of 196

1.How do you find the multiples of 196?

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2.What is the LCM of 14 and 196?

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3.What are the real-life applications of Multiples of 196?

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4.Are multiples of 196 finite or infinite?

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5.Is there any odd multiple of 196?

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Important Glossaries for Multiples of 196

  • Multiple: A multiple represents the product of a number that may be multiplied by an integer. For example, multiples of 196 include 196, 392, 588, 784, etc.
     
  • Number pattern: This refers to how numbers are listed. It should follow a certain sequence. Multiples of 196 are the numbers that consist of the number pattern of 196.
     
  • Even number: An even number refers to any number that can be divisible by 2 without leaving any remainder. The last digits of even numbers are 0, 2, 4, 6, or 8. All multiples of 196 are even numbers.
     
  • Divisor: It refers to any number by which another number can be divided without leaving any remainder. 1, 2, 4, 7, 14, 28, 49, 98, and 196 are the divisors of 196.
     
  • Factor: A factor is a number that divides another number completely without leaving a remainder. For example, factors of 196 include 1, 2, 4, 7, 14, 28, 49, 98, and 196.
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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

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Fun Fact

: She has songs for each table which helps her to remember the tables

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