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Last updated on May 26th, 2025

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Factors of -68

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Factors are 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 -68, how they are used in real life, and tips to learn them quickly.

Factors of -68 for Indian Students
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What are the Factors of -68?

The numbers that divide -68 evenly are known as factors of -68.

 

A factor of -68 is a number that divides the number without a remainder.

 

The positive factors of 68 are 1, 2, 4, 17, 34, and 68.

 

The negative factors of -68: -1, -2, -4, -17, -34, and -68.

 

Prime factors of 68: 2 and 17.

 

Prime factorization of 68: 2² × 17.

 

The sum of positive factors of 68: 1 + 2 + 4 + 17 + 34 + 68 = 126

factors of -68

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How to Find Factors of -68?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we identify the pairs of numbers that multiply to give 68. Identifying the numbers that are multiplied to get the number 68 is the multiplication method.

 

Step 1: Multiply 68 by 1, 68 × 1 = 68.

 

Step 2: Check for other numbers that give 68 after multiplying 2 × 34 = 68 4 × 17 = 68

 

Therefore, the positive factor pairs of 68 are: (1, 68), (2, 34), and (4, 17).

 

All these factor pairs result in 68.

 

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers by 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 68 by 1, 68 ÷ 1 = 68.

 

Step 2: Continue dividing 68 by the numbers until the remainder becomes 0.

68 ÷ 1 = 68

68 ÷ 2 = 34

68 ÷ 4 = 17

 

Therefore, the factors of 68 are: 1, 2, 4, 17, 34, 68.

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Prime Factors and Prime Factorization

The factors can be found by dividing it by prime numbers. We can find the prime factors using the following methods:

  • Using prime factorization
  • Using a factor tree

 

Using Prime Factorization: In this process, prime factors of 68 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.

68 ÷ 2 = 34

34 ÷ 2 = 17

17 ÷ 17 = 1

 

The prime factors of 68 are 2 and 17.

 

The prime factorization of 68 is: 2² × 17.

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Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows 

 

Step 1: Firstly, 68 is divided by 2 to get 34.

 

Step 2: Now divide 34 by 2 to get 17. Here, 17 is the smallest prime number that cannot be divided anymore.

 

So, the prime factorization of 68 is: 2² × 17.

 

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 68: (1, 68), (2, 34), and (4, 17).

 

Negative factor pairs of -68: (-1, -68), (-2, -34), and (-4, -17).

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Common Mistakes and How to Avoid Them in Factors of -68

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

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Forgetting the number itself and 1 is a factor

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Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every whole number. Always remember to include 1 and the number itself.

 

For example, in factors of 68, 1 and 68 are also factors.

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Factors of -68 Examples

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Problem 1

There are 4 friends and 68 marbles. How will they divide them equally?

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They will get 17 marbles each.

Explanation

To divide the marbles equally, we need to divide the total marbles by the number of friends.

68/4 = 17

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Problem 2

A garden is rectangular, the length of the garden is 17 meters, and the total area is 68 square meters. Find the width.

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4 meters.

Explanation

To find the width of the garden, we use the formula, Area = length × width 68 = 17 × width

To find the value of width, we need to shift 17 to the left side.

68/17 = width

Width = 4.

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Problem 3

There are 2 baskets and 68 apples. How many apples will be in each basket?

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Each basket will have 34 apples.

Explanation

To find the apples in each basket, divide the total apples by the number of baskets.

68/2 = 34

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Problem 4

In a class, there are 68 pencils, and 4 boxes. How many pencils are there in each box?

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There are 17 pencils in each box.

Explanation

Dividing the pencils by the total boxes, we will get the number of pencils in each box.

68/4 = 17

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Problem 5

68 chairs need to be arranged in 2 rows. How many chairs will go in each row?

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Each row has 34 chairs.

Explanation

Divide total chairs by rows.

68/2 = 34

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FAQs on Factors of -68

1.What are the factors of -68?

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2.Mention the prime factors of 68.

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3.Is 68 a multiple of 4?

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4.Mention the factor pairs of -68?

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5.What is the square of 68?

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6.How can children in India use numbers in everyday life to understand Factors of -68?

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7.What are some fun ways kids in India can practice Factors of -68 with numbers?

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8.What role do numbers and Factors of -68 play in helping children in India develop problem-solving skills?

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9.How can families in India create number-rich environments to improve Factors of -68 skills?

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Professor Greenline from BrightChamps

Important Glossaries for Factors of -68

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 68 are 1, 2, 4, 17, 34, and 68.

 

  • Prime factors: The factors which are prime numbers. For example, 2 and 17 are prime factors of 68.

 

  • Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 68 is 2² × 17.

 

  • 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 68 are (1, 68), (2, 34), etc.

 

  • Negative factors: Factors that are negative counterparts of the positive factors. For example, -1, -2, -4, -17, -34, and -68 are the negative factors of -68.
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About BrightChamps in India

At BrightChamps, numbers mean more than just digits—they open pathways to endless opportunities! We’re here to help children all over India grasp crucial math skills, focusing on today’s Factors of -68 with a special look at factors—in a way that’s enjoyable, simple, and interactive. Whether your child is calculating the speed of a train passing by, following scores in a cricket match, or managing their pocket money for new gadgets, knowing numbers helps build their confidence in daily life. Our hands-on lessons keep learning fun and easy. Since kids in India learn in many ways, we customize lessons to fit each learner. From Mumbai’s lively markets to Delhi’s vibrant streets, BrightChamps makes math meaningful and exciting all across India. Let’s turn factors into a fun part of every child’s math story!
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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.

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Fun Fact

: She loves to read number jokes and games.

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