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Last updated on May 26th, 2025

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Factors of 1924

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Factors are the 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 1924, how they are used in real life, and tips to learn them quickly.

Factors of 1924 for Global Students
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What are the Factors of 1924?

The numbers that divide 1924 evenly are known as factors of 1924.

 

A factor of 1924 is a number that divides the number without a remainder.

 

The factors of 1924 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 361, 532, 722, 1444, and 1924.

 

Negative factors of 1924: -1, -2, -4, -7, -14, -19, -28, -38, -76, -133, -266, -361, -532, -722, -1444, and -1924.

 

Prime factors of 1924: 2, 7, and 19.

 

Prime factorization of 1924: 22 × 7 × 19.

 

The sum of factors of 1924: 1 + 2 + 4 + 7 + 14 + 19 + 28 + 38 + 76 + 133 + 266 + 361 + 532 + 722 + 1444 + 1924 = 5578

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How to Find Factors of 1924?

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 need to identify the pairs of numbers that are multiplied to give 1924. Identifying the numbers which are multiplied to get the number 1924 is the multiplication method.

 

Step 1: Multiply 1924 by 1, 1924 × 1 = 1924.

 

Step 2: Check for other numbers that give 1924 after multiplying

2 × 962 = 1924

4 × 481 = 1924

7 × 274 = 1924

14 × 137 = 1924

19 × 101 = 1924

 

Therefore, the positive factor pairs of 1924 are: (1, 1924), (2, 962), (4, 481), (7, 274), (14, 137), and (19, 101). For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with 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 the simple division method

 

Step 1: Divide 1924 by 1, 1924 ÷ 1 = 1924.

 

Step 2: Continue dividing 1924 by the numbers until the remainder becomes 0.

1924 ÷ 1 = 1924

1924 ÷ 2 = 962

1924 ÷ 4 = 481

1924 ÷ 7 = 274

1924 ÷ 14 = 137

1924 ÷ 19 = 101

 

Therefore, the factors of 1924 are: 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 361, 532, 722, 1444, and 1924.

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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 a factor tree

 

Using Prime Factorization: In this process, prime factors of 1924 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1924 ÷ 2 = 962

962 ÷ 2 = 481

481 ÷ 7 = 137

137 ÷ 19 = 1

 

The prime factors of 1924 are 2, 7, and 19.

 

The prime factorization of 1924 is: 22 × 7 × 19.

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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, 1924 is divided by 2 to get 962.

 

Step 2: Now divide 962 by 2 to get 481.

 

Step 3: Then divide 481 by 7 to get 137.

 

Step 4: Divide 137 by 19 to get 1. The prime factorization of 1924 is: 22 × 7 × 19.

 

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 1924: (1, 1924), (2, 962), (4, 481), (7, 274), (14, 137), (19, 101).

 

Negative factor pairs of 1924: (-1, -1924), (-2, -962), (-4, -481), (-7, -274), (-14, -137), (-19, -101).

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Common Mistakes and How to Avoid Them in Factors of 1924

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 number. Always remember to include 1 and the number itself.

 

For example, in factors of 1924, 1 and 1924 are also factors.

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Factors of 1924 Examples

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Problem 1

There are 7 teams and 1924 apples. How will the apples be divided equally?

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Each team will get 274 apples.

Explanation

To divide the apples equally, we need to divide the total apples by the number of teams.

1924/7 = 274

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Problem 2

A parking lot is rectangular, the length of the lot is 38 meters and the total area is 1924 square meters. Find the width?

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The width is 51 meters.

Explanation

To find the width of the parking lot, we use the formula, Area = length × width

1924 = 38 × width

To find the value of width, we need to shift 38 to the left side.

1924/38 = width

Width = 51.

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Problem 3

There are 266 students and 1924 books. How many books will each student get?

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Each student will get 7 books.

Explanation

To find the number of books each student gets, divide the total books by the number of students.

1924/266 = 7

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Problem 4

In a class of 38 students, there is a total of 1924 candies. How many candies are there for each student?

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Each student will get 51 candies.

Explanation

Dividing the total candies by the number of students, we will get the number of candies per student.

1924/38 = 51

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Problem 5

1924 chairs need to be arranged in 19 rows. How many chairs will be in each row?

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Each row will have 101 chairs.

Explanation

Divide the total number of chairs by the number of rows.

1924/19 = 101

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FAQs on Factors of 1924

1.What are the factors of 1924?

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2.Mention the prime factors of 1924.

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3.Is 1924 a multiple of 14?

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4.Mention the factor pairs of 1924?

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5.What is the square of 1924?

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Important Glossaries for Factors of 1924

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1924 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 361, 532, 722, 1444, and 1924.

 

  • Prime factors: The factors which are prime numbers. For example, 2, 7, and 19 are prime factors of 1924.

 

  • 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 1924 are (1, 1924), (2, 962), etc.

 

  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1924 is 22 × 7 × 19.

 

  • Negative factors: These are the negative counterparts of the positive factors of a number. For example, the negative factors of 1924 are -1, -2, -4, -7, -14, -19, -28, -38, -76, -133, -266, -361, -532, -722, -1444, and -1924.
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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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