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Last updated on May 26th, 2025

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Factors of 1968

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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 1968, how they are used in real life, and the tips to learn them quickly.

Factors of 1968 for Global Students
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What are the Factors of 1968?

The numbers that divide 1968 evenly are known as factors of 1968.

 

A factor of 1968 is a number that divides the number without remainder.

 

The factors of 1968 are 1, 2, 3, 4, 6, 12, 164, 246, 328, 492, 656, 984, and 1968.

 

Negative factors of 1968: -1, -2, -3, -4, -6, -12, -164, -246, -328, -492, -656, -984, and -1968.

 

Prime factors of 1968: 2 and 3.

 

Prime factorization of 1968: 23 × 3 × 41.

 

The sum of factors of 1968: 1 + 2 + 3 + 4 + 6 + 12 + 164 + 246 + 328 + 492 + 656 + 984 + 1968 = 4866

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How to Find Factors of 1968?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1968. Identifying the numbers which are multiplied to get the number 1968 is the multiplication method.

 

Step 1: Multiply 1968 by 1, 1968 × 1 = 1968.

 

Step 2: Check for other numbers that give 1968 after multiplying

 

2 × 984 = 1968

3 × 656 = 1968

4 × 492 = 1968

6 × 328 = 1968

12 × 164 = 1968

 

Therefore, the positive factor pairs of 1968 are: (1, 1968), (2, 984), (3, 656), (4, 492), (6, 328), (12, 164).

 

All these factor pairs result in 1968.

 

For every positive factor, there is a negative factor.

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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 1968 by 1, 1968 ÷ 1 = 1968.

 

Step 2: Continue dividing 1968 by the numbers until the remainder becomes 0.

 

1968 ÷ 1 = 1968

1968 ÷ 2 = 984

1968 ÷ 3 = 656

1968 ÷ 4 = 492

1968 ÷ 6 = 328

1968 ÷ 12 = 164

 

Therefore, the factors of 1968 are: 1, 2, 3, 4, 6, 12, 164, 246, 328, 492, 656, 984, 1968.

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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 1968 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

1968 ÷ 2 = 984

984 ÷ 2 = 492

492 ÷ 2 = 246

246 ÷ 3 = 82

82 ÷ 41 = 2

41 ÷ 41 = 1

 

The prime factors of 1968 are 2, 3, and 41.

 

The prime factorization of 1968 is: 23 × 3 × 41.

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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, 1968 is divided by 2 to get 984.

 

Step 2: Now divide 984 by 2 to get 492.

 

Step 3: Then divide 492 by 2 to get 246.

 

Step 4: Divide 246 by 3 to get 82.

 

Step 5: Divide 82 by 41 to get 2. Here, 2 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1968 is: 23 × 3 × 41.

 

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 1968: (1, 1968), (2, 984), (3, 656), (4, 492), (6, 328), (12, 164).

 

Negative factor pairs of 1968: (-1, -1968), (-2, -984), (-3, -656), (-4, -492), (-6, -328), (-12, -164).

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Common Mistakes and How to Avoid Them in Factors of 1968

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 the factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 1968, 1 and 1968 are also factors.

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Factors of 1968 Examples

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Problem 1

There are 12 friends and 1968 candies. How will they divide it equally?

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They will get 164 candies each.

Explanation

To divide the candies equally, we need to divide the total candies with the number of friends.

 

1968/12 = 164

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Problem 2

A field is rectangular, the length of the field is 41 meters and the total area is 1968 square meters. Find the width?

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48 meters.

Explanation

To find the width of the field, we use the formula,

 

Area = length × width

 

1968 = 41 × width

 

To find the value of width, we need to shift 41 to the left side.

 

1968/41 = width

 

Width = 48.

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Problem 3

There are 6 bags and 1968 cookies. How many cookies will be in each bag?

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Each bag will have 328 cookies.

Explanation

To find the cookies in each bag, divide the total cookies with the bags.

 

1968/6 = 328

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Problem 4

In a class, there are 1968 students, and 12 groups. How many students are there in each group?

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There are 164 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.

 

1968/12 = 164

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Problem 5

1968 books need to be arranged in 164 shelves. How many books will go on each shelf?

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Each of the shelves has 12 books.

Explanation

Divide total books with shelves.

 

1968/164 = 12

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FAQs on Factors of 1968

1.What are the factors of 1968?

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2.Mention the prime factors of 1968.

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3.Is 1968 a multiple of 6?

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4.Mention the factor pairs of 1968?

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5.What is the square of 1968?

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Important Glossaries for Factor of 1968

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1968 are 1, 2, 3, 4, 6, 12, 164, 246, 328, 492, 656, 984, and 1968.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 41 are prime factors of 1968.
     
  • 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 1968 are (1, 1968), (2, 984), etc.
     
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1968 is 23 × 3 × 41.
     
  • Multiple: A number that can be divided by another number without a remainder. For example, 1968 is a multiple of 6.
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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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