125 LearnersLast updated on May 26th, 2025
Factors of 1974
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 1974, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1974?
The numbers that divide 1974 evenly are known as factors of 1974.
A factor of 1974 is a number that divides the number without a remainder.
The factors of 1974 are 1, 2, 3, 6, 9, 18, 109, 218, 327, 654, 987, and 1974.
Negative factors of 1974: -1, -2, -3, -6, -9, -18, -109, -218, -327, -654, -987, and -1974.
Prime factors of 1974: 2, 3, and 109.
Prime factorization of 1974: 2 × 3^2 × 109.
The sum of factors of 1974: 1 + 2 + 3 + 6 + 9 + 18 + 109 + 218 + 327 + 654 + 987 + 1974 = 4308
How to Find Factors of 1974?
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 1974. Identifying the numbers which are multiplied to get the number 1974 is the multiplication method.
Step 1: Multiply 1974 by 1, 1974 × 1 = 1974.
Step 2: Check for other numbers that give 1974 after multiplying
2 × 987 = 1974
3 × 658 = 1974
6 × 329 = 1974
9 × 219 = 1974
18 × 109 = 1974
Therefore, the positive factor pairs of 1974 are: (1, 1974), (2, 987), (3, 658), (6, 329), (9, 219), (18, 109).
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 a simple division method
Step 1: Divide 1974 by 1, 1974 ÷ 1 = 1974.
Step 2: Continue dividing 1974 by the numbers until the remainder becomes 0.
1974 ÷ 1 = 1974
1974 ÷ 2 = 987
1974 ÷ 3 = 658
1974 ÷ 6 = 329
1974 ÷ 9 = 219
1974 ÷ 18 = 109
Therefore, the factors of 1974 are: 1, 2, 3, 6, 9, 18, 109, 218, 327, 654, 987, 1974.
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 1974 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1974 ÷ 2 = 987
987 ÷ 3 = 329
329 ÷ 3 = 109
109 ÷ 109 = 1
The prime factors of 1974 are 2, 3, and 109.
The prime factorization of 1974 is: 2 × 3^2 × 109.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1974 is divided by 2 to get 987.
Step 2: Now divide 987 by 3 to get 329. Step 3: Then divide 329 by 3 to get 109. Here, 109 is a prime number, that cannot be divided anymore. So, the prime factorization of 1974 is: 2 × 3^2 × 109.
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 1974: (1, 1974), (2, 987), (3, 658), (6, 329), (9, 219), and (18, 109).
Negative factor pairs of 1974: (-1, -1974), (-2, -987), (-3, -658), (-6, -329), (-9, -219), and (-18, -109).
Common Mistakes and How to Avoid Them in Factors of 1974
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 the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1974, 1 and 1974 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1974 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1974/1.5 = 1316, 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 1974 are prime numbers.
For example, 2, 3, and 109 are the prime factors of 1974, but it has other factors like 6, 18.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1974 as 2 × 3^2 × 109 and missing all the key factors.
Factors of 1974 Examples
Problem 1
A theater has 18 rows and 1974 seats. How many seats are there in each row?
There are 109 seats in each row.
Explanation
To find the seats in each row, we need to divide the total seats by the number of rows.
1974/18 = 109
Problem 2
A garden is rectangular, the width of the garden is 9 meters and the total area is 1974 square meters. Find the length?
219 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1974 = length × 9
To find the value of length, we need to shift 9 to the left side.
1974/9 = length
Length = 219.
Problem 3
There are 3 buses and 1974 passengers. How many passengers will be in each bus?
Each bus will have 658 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the buses.
1974/3 = 658
Problem 4
In a school, there are 1974 students, and 6 classes. How many students are there in each class?
There are 329 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
1974/6 = 329
Problem 5
1974 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 219 books.
Explanation
Divide total books by shelves.
1974/9 = 219
FAQs on Factors of 1974
1.What are the factors of 1974?
2.Mention the prime factors of 1974.
3.Is 1974 a multiple of 3?
4.Mention the factor pairs of 1974?
5.What is the square of 1974?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 1974?
7.What are some fun ways kids in Vietnam can practice Factors of 1974 with numbers?
8.What role do numbers and Factors of 1974 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 1974 skills?
Important Glossaries for Factors of 1974
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1974 are 1, 2, 3, 6, 9, 18, 109, 218, 327, 654, 987, and 1974.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 109 are prime factors of 1974.
- 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 1974 are (1, 1974), (2, 987), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1974 is 2 × 32 × 109.
- Multiple: A multiple is a number that can be divided by another number without leaving a remainder. For example, 1974 is a multiple of 3.
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About BrightChamps in Vietnam
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.
