120 LearnersLast updated on May 26th, 2025
Factors of 1961
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 1961, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1961?
The numbers that divide 1961 evenly are known as factors of 1961.
A factor of 1961 is a number that divides the number without remainder.
The factors of 1961 are 1, 37, 53, and 1961.
Negative factors of 1961: -1, -37, -53, and -1961.
Prime factors of 1961: 37 and 53.
Prime factorization of 1961: 37 × 53.
The sum of factors of 1961: 1 + 37 + 53 + 1961 = 2052
How to Find Factors of 1961?
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 1961. Identifying the numbers which are multiplied to get the number 1961 is the multiplication method.
Step 1: Multiply 1961 by 1, 1961 × 1 = 1961.
Step 2: Check for other numbers that give 1961 after multiplying 37 × 53 = 1961
Therefore, the positive factor pairs of 1961 are: (1, 1961) and (37, 53).
All these factor pairs result in 1961.
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 1961 by 1, 1961 ÷ 1 = 1961.
Step 2: Continue dividing 1961 by the numbers until the remainder becomes 0.
1961 ÷ 1 = 1961
1961 ÷ 37 = 53
1961 ÷ 53 = 37
Therefore, the factors of 1961 are: 1, 37, 53, and 1961.
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 1961 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1961 ÷ 37 = 53
53 ÷ 53 = 1
The prime factors of 1961 are 37 and 53.
The prime factorization of 1961 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, 1961 is divided by 37 to get 53.
Step 2: Now divide 53 by 53 to get 1. Here, 53 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1961 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 1961: (1, 1961) and (37, 53).
Negative factor pairs of 1961: (-1, -1961) and (-37, -53).
Common Mistakes and How to Avoid Them in Factors of 1961
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 1961, 1 and 1961 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 1961 consist of -1, -37, 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 1961/1.5 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 1961 are prime numbers.
For example, 37 and 53 are the prime factors of 1961, but it has other factors like 1 and 1961.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1961 as 37 × 53 and missing all the key factors.
Factors of 1961 Examples
Problem 1
There is a wagon carrying 1961 kilograms of goods. How many full crates of 37 kilograms each can the wagon carry?
The wagon can carry 53 full crates.
Explanation
To find the number of crates, divide the total weight by the weight of each crate.
1961/37 = 53
Problem 2
A rectangular garden has a length of 53 meters and a total area of 1961 square meters. Find the width.
37 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1961 = 53 × width
To find the value of width, we need to shift 53 to the left side.
1961/53 = width
Width = 37.
Problem 3
There are 37 shelves and 1961 books. How many books will be on each shelf?
Each shelf will have 53 books.
Explanation
To find the books on each shelf, divide the total books by the number of shelves.
1961/37 = 53
Problem 4
A conference room has 1961 chairs and 53 tables. How many chairs are there per table?
There are 37 chairs per table.
Explanation
Dividing the chairs by the total tables, we will get the number of chairs per table.
1961/53 = 37
Problem 5
1961 apples need to be placed in 53 baskets. How many apples will go in each basket?
Each basket will have 37 apples.
Explanation
Divide total apples by baskets.
1961/53 = 37
FAQs on Factors of 1961
1.What are the factors of 1961?
2.Mention the prime factors of 1961.
3.Is 1961 a multiple of 53?
4.Mention the factor pairs of 1961?
5.What is the square of 1961?
Important Glossaries for Factor of 1961
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1961 are 1, 37, 53, and 1961.
- Prime factors: The factors which are prime numbers. For example, 37 and 53 are prime factors of 1961.
- 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 1961 are (1, 1961) and (37, 53).
- Multiple: A number that can be divided by another number without a remainder. For example, 1961 is a multiple of 53.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 1961 is 37 × 53.
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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.
