103 LearnersLast updated on May 26th, 2025
Factors of 1984
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 1984, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1984?
The numbers that divide 1984 evenly are known as factors of 1984.
A factor of 1984 is a number that divides the number without a remainder.
The factors of 1984 are 1, 2, 4, 8, 16, 31, 62, 62, 124, 248, 496, 992, and 1984.
Negative factors of 1984: -1, -2, -4, -8, -16, -31, -62, -124, -248, -496, -992, and -1984.
Prime factors of 1984: 2 and 31.
Prime factorization of 1984: 24 × 31.
The sum of factors of 1984: 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 + 496 + 992 + 1984 = 3968
How to Find Factors of 1984?
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 1984. Identifying the numbers which are multiplied to get the number 1984 is the multiplication method.
Step 1: Multiply 1984 by 1, 1984 × 1 = 1984.
Step 2: Check for other numbers that give 1984 after multiplying
2 × 992 = 1984
4 × 496 = 1984
8 × 248 = 1984
16 × 124 = 1984
31 × 64 = 1984
Therefore, the positive factor pairs of 1984 are: (1, 1984), (2, 992), (4, 496), (8, 248), (16, 124), (31, 64).
For every positive factor, there is a negative factor.
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 1984 by 1, 1984 ÷ 1 = 1984.
Step 2: Continue dividing 1984 by the numbers until the remainder becomes 0.
1984 ÷ 1 = 1984
1984 ÷ 2 = 992
1984 ÷ 4 = 496
1984 ÷ 8 = 248
1984 ÷ 16 = 124
1984 ÷ 31 = 64
Therefore, the factors of 1984 are: 1, 2, 4, 8, 16, 31, 62, 124, 248, 496, 992, 1984.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1984 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
1984 ÷ 2 = 992
992 ÷ 2 = 496
496 ÷ 2 = 248
248 ÷ 2 = 124
124 ÷ 2 = 62
62 ÷ 2 = 31
31 ÷ 31 = 1
The prime factors of 1984 are 2 and 31.
The prime factorization of 1984 is: 26 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1984 is divided by 2 to get 992.
Step 2: Now divide 992 by 2 to get 496.
Step 3: Then divide 496 by 2 to get 248.
Step 4: Divide 248 by 2 to get 124.
Step 5: Divide 124 by 2 to get 62.
Step 6: Divide 62 by 2 to get 31. 31 is a prime number that cannot be divided anymore.
So, the prime factorization of 1984 is: 26 × 31.
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 1984: (1, 1984), (2, 992), (4, 496), (8, 248), (16, 124), and (31, 64).
Negative factor pairs of 1984: (-1, -1984), (-2, -992), (-4, -496), (-8, -248), (-16, -124), and (-31, -64).
Common Mistakes and How to Avoid Them in Factors of 1984
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 1984, 1 and 1984 are also factors.
Factors of 1984 Examples
Problem 1
There are 16 teams and 1984 participants. How will they divide participants equally among the teams?
Each team will have 124 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1984/16 = 124
Problem 2
A rectangular garden has a width of 31 meters and a total area of 1984 square meters. Find the length of the garden.
64 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1984 = length × 31
To find the value of length, we need to divide the area by the width.
1984/31 = length
Length = 64.
Problem 3
There are 248 gift bags and 1984 candies. How many candies will be in each bag?
Each bag will have 8 candies.
Explanation
To find the candies in each bag, divide the total candies by the number of bags.
1984/248 = 8
Problem 4
In a conference, there are 1984 attendees and 62 tables. How many attendees are there per table?
There are 32 attendees per table.
Explanation
Dividing the attendees by the total tables, we will get the number of attendees per table.
1984/62 = 32
Problem 5
1984 chairs need to be arranged in 124 rows. How many chairs will go in each row?
Each row will have 16 chairs.
Explanation
Divide the total chairs by the number of rows.
1984/124 = 16
FAQs on Factors of 1984
1.What are the factors of 1984?
2.Mention the prime factors of 1984.
3.Is 1984 a multiple of 16?
4.Mention the factor pairs of 1984?
5.What is the square of 1984?
6.How can children in Canada use numbers in everyday life to understand Factors of 1984?
7.What are some fun ways kids in Canada can practice Factors of 1984 with numbers?
8.What role do numbers and Factors of 1984 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1984 skills?
Important Glossaries for Factors of 1984
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1984 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496, 992, and 1984.
- Prime factors: The factors which are prime numbers. For example, 2 and 31 are prime factors of 1984.
- 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 1984 are (1, 1984), (2, 992), etc.
- Prime Factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1984 is 26 × 31.
- Multiple: A number that can be divided by another number without a remainder. For example, 1984 is a multiple of 16.
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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
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