120 LearnersLast updated on May 26th, 2025
Factors of 1924
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.
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
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
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.
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.
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.
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).
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
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 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.
Mistake 2
Missing Negative Factors
We often only mention positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 1924 include -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes incorrectly include fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 1924/1.5 = 1282.6667, and it 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 1924 are prime numbers. 2, 7, and 19 are the prime factors of 1924, but it has other factors like 4, 14.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 1924 down as 22 × 7 × 19 and missing all the key factors.
Factors of 1924 Examples
Problem 1
There are 7 teams and 1924 apples. How will the apples be divided equally?
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
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?
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.
Problem 3
There are 266 students and 1924 books. How many books will each student get?
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
Problem 4
In a class of 38 students, there is a total of 1924 candies. How many candies are there for each student?
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
Problem 5
1924 chairs need to be arranged in 19 rows. How many chairs will be in each row?
Each row will have 101 chairs.
Explanation
Divide the total number of chairs by the number of rows.
1924/19 = 101
FAQs on Factors of 1924
1.What are the factors of 1924?
2.Mention the prime factors of 1924.
3.Is 1924 a multiple of 14?
4.Mention the factor pairs of 1924?
5.What is the square of 1924?
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.
Fun Fact
: She loves to read number jokes and games.
