139 LearnersLast updated on May 26th, 2025
Factors of 1963
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 1963, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1963?
The numbers that divide 1963 evenly are known as factors of 1963.
A factor of 1963 is a number that divides the number without remainder.
The factors of 1963 are 1, 37, 53, and 1963.
Negative factors of 1963: -1, -37, -53, and -1963.
Prime factors of 1963: 37 and 53.
Prime factorization of 1963: 37 × 53.
The sum of factors of 1963: 1 + 37 + 53 + 1963 = 2054
How to Find Factors of 1963?
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 1963. Identifying the numbers which are multiplied to get the number 1963 is the multiplication method.
Step 1: Multiply 1963 by 1, 1963 × 1 = 1963.
Step 2: Check for other numbers that give 1963 after multiplying 37 × 53 = 1963
Therefore, the positive factor pairs of 1963 are: (1, 1963) and (37, 53).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1963 by 1, 1963 ÷ 1 = 1963.
Step 2: Continue dividing 1963 by the numbers until the remainder becomes 0.
1963 ÷ 1 = 1963
1963 ÷ 37 = 53
1963 ÷ 53 = 37
Therefore, the factors of 1963 are: 1, 37, 53, 1963.
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 1963 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1963 ÷ 37 = 53
53 ÷ 53 = 1
The prime factors of 1963 are 37 and 53.
The prime factorization of 1963 is: 37 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1963 is divided by 37 to get 53.
Step 2: Now divide 53 by 53 to get 1. Here, 53 is a prime number, and it cannot be divided anymore. So, the prime factorization of 1963 is: 37 × 53.
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 1963: (1, 1963) and (37, 53).
Negative factor pairs of 1963: (-1, -1963) and (-37, -53).
Common Mistakes and How to Avoid Them in Factors of 1963
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 1963, 1 and 1963 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 1963 consist of -1, -37, -53, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1963/1.5 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 1963 are prime numbers.
For example, 37 and 53 are the prime factors of 1963, but it also has other factors like 1 and 1963.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1963 as 37 × 53 and missing all the key factors.
Factors of 1963 Examples
Problem 1
There are 37 students and 1963 candies. How will they divide it equally?
They will get 53 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
1963/37 = 53
Problem 2
A rectangular field has a length of 37 meters and a total area of 1963 square meters. Find the width.
53 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1963 = 37 × width
To find the value of width, we need to shift 37 to the left side.
1963/37 = width
Width = 53.
Problem 3
There are 53 tables and 1963 chairs. How many chairs will be at each table?
Each table will have 37 chairs.
Explanation
To find the chairs at each table, divide the total chairs by the tables.
1963/53 = 37
Problem 4
In a class, there are 1963 students, and they are split into 53 groups. How many students are there in each group?
There are 37 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1963/53 = 37
Problem 5
1963 books need to be arranged in 37 shelves. How many books will go on each shelf?
Each of the shelves has 53 books.
Explanation
Divide total books by shelves.
1963/37 = 53
FAQs on Factors of 1963
1.What are the factors of 1963?
2.Mention the prime factors of 1963.
3.Is 1963 a multiple of 37?
4.Mention the factor pairs of 1963?
5.What is the square of 1963?
Important Glossaries for Factor of 1963
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1963 are 1, 37, 53, and 1963.
- Prime factors: The factors which are prime numbers. For example, 37 and 53 are prime factors of 1963.
- 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 1963 are (1, 1963) and (37, 53).
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1963 is 37 × 53.
- Negative factors: Factors that are negative but still divide the number without a remainder. For example, -1, -37, -53, and -1963 are negative factors of 1963.
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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.
