123 LearnersLast updated on May 26th, 2025
Factors of 1964
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 1964, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1964?
The numbers that divide 1964 evenly are known as factors of 1964.
A factor of 1964 is a number that divides the number without remainder.
The factors of 1964 are 1, 2, 4, 491, 982, and 1964.
Negative factors of 1964: -1, -2, -4, -491, -982, and -1964.
Prime factors of 1964: 2 and 491.
Prime factorization of 1964: 2² × 491.
The sum of factors of 1964: 1 + 2 + 4 + 491 + 982 + 1964 = 3444
How to Find Factors of 1964?
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
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1964. Identifying the numbers which are multiplied to get the number 1964 is the multiplication method.
Step 1: Multiply 1964 by 1, 1964 × 1 = 1964.
Step 2: Check for other numbers that give 1964 after multiplying
2 × 982 = 1964
4 × 491 = 1964
Therefore, the positive factor pairs of 1964 are: (1, 1964), (2, 982), and (4, 491).
All these factor pairs result in 1964.
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 1964 by 1, 1964 ÷ 1 = 1964.
Step 2: Continue dividing 1964 by the numbers until the remainder becomes 0.
1964 ÷ 1 = 1964
1964 ÷ 2 = 982
1964 ÷ 4 = 491
Therefore, the factors of 1964 are: 1, 2, 4, 491, 982, and 1964.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1964 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1964 ÷ 2 = 982
982 ÷ 2 = 491
491 is a prime number, so it cannot be divided further by any number other than 1 and itself.
The prime factors of 1964 are 2 and 491.
The prime factorization of 1964 is: 2² × 491.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1964 is divided by 2 to get 982.
Step 2: Now divide 982 by 2 to get 491. Here, 491 is a prime number that cannot be divided anymore. So, the prime factorization of 1964 is: 2² × 491.
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 1964: (1, 1964), (2, 982), and (4, 491).
Negative factor pairs of 1964: (-1, -1964), (-2, -982), and (-4, -491).
Common Mistakes and How to Avoid Them in Factors of 1964
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 1964, 1 and 1964 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 1964 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1964/1.5 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 1964 are prime numbers.
For example, 2 and 491 are the prime factors of 1964, but it has other factors like 4.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1964 as 2² × 491 and missing all the key factors.
Factors of 1964 Examples
Problem 1
There are 2 teams and 1964 points. How will they divide it equally?
They will get 982 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
1964/2 = 982
Problem 2
A plot is rectangular, the length of the plot is 491 meters and the total area is 1964 square meters. Find the width?
4 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
1964 = 491 × width
To find the value of width, we need to shift 491 to the left side.
1964/491 = width
Width = 4.
Problem 3
There are 4 boxes and 1964 candies. How many candies will be in each box?
Each box will have 491 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
1964/4 = 491
Problem 4
In a competition, there are 1964 participants, and 491 groups. How many participants are there in each group?
There are 4 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
1964/491 = 4
Problem 5
1964 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 982 books.
Explanation
Divide the total books by the number of shelves.
1964/2 = 982
FAQs on Factors of 1964
1.What are the factors of 1964?
2.Mention the prime factors of 1964.
3.Is 1964 a multiple of 4?
4.Mention the factor pairs of 1964?
5.What is the square of 1964?
6.How can children in Oman use numbers in everyday life to understand Factors of 1964?
7.What are some fun ways kids in Oman can practice Factors of 1964 with numbers?
8.What role do numbers and Factors of 1964 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Factors of 1964 skills?
Important Glossaries for Factor of 1964
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1964 are 1, 2, 4, 491, 982, and 1964.
- Prime factors: The factors which are prime numbers. For example, 2 and 491 are prime factors of 1964.
- 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 1964 are (1, 1964), (2, 982), etc.
- Prime factorization: The expression of a number as a product of its prime numbers. For example, the prime factorization of 1964 is 2² × 491.
- Division method: A technique used to find factors by dividing the number by integers until the remainder is zero. For example, dividing 1964 by 1, 2, 4, etc., to find factors.
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About BrightChamps in Oman
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.
