133 LearnersLast updated on May 26th, 2025
Factors of 961
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 961, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 961?
The numbers that divide 961 evenly are known as factors of 961.
A factor of 961 is a number that divides the number without remainder.
The factors of 961 are 1, 31, and 961.
Negative factors of 961: -1, -31, and -961.
Prime factor of 961: 31.
Prime factorization of 961: 31 × 31.
The sum of factors of 961: 1 + 31 + 961 = 993
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How to Find Factors of 961?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factor 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 961. Identifying the numbers which are multiplied to get the number 961 is the multiplication method.
Step 1: Multiply 961 by 1, 961 × 1 = 961.
Step 2: Check for other numbers that give 961 after multiplying 31 × 31 = 961
Therefore, the positive factor pairs of 961 are: (1, 961) and (31, 31).
All these factor pairs result in 961.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 961 by 1, 961 ÷ 1 = 961.
Step 2: Continue dividing 961 by numbers until the remainder becomes 0.
961 ÷ 1 = 961
961 ÷ 31 = 31
Therefore, the factors of 961 are: 1, 31, and 961.
Prime Factor and Prime Factorization
The factors can be found by dividing it with a prime number. We can find the prime factor using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, the prime factor of 961 divides the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
961 ÷ 31 = 31
31 ÷ 31 = 1
The prime factor of 961 is 31.
The prime factorization of 961 is: 31 × 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, 961 is divided by 31 to get 31.
Step 2: Now divide 31 by 31 to get 1. Here, 31 is the only prime number that divides 961 completely.
So, the prime factorization of 961 is: 31 × 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 961: (1, 961) and (31, 31).
Negative factor pairs of 961: (-1, -961) and (-31, -31).
Common Mistakes and How to Avoid Them in Factors of 961
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 961, 1 and 961 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 961 consist of -1, -31, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 0.5 as a factor, because 961/0.5 = 1922, 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 961 are prime numbers.
For example, 31 is the prime factor of 961, but it has other factors like 1 and 961.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 961 as 31 × 31 and missing all the key factors.
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Factors of 961 Examples
Problem 1
There are 31 students and 961 apples. How will they divide it equally?
They will get 31 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of students.
961/31 = 31
Problem 2
A square garden has an area of 961 square meters. What is the length of one side?
31 meters.
Explanation
To find the length of one side of the square, we use the square root of the area.
The square root of 961 is 31.
31 × 31 = 961
Problem 3
There are 961 marbles and 31 jars. How many marbles will be in each jar?
Each jar will have 31 marbles.
Explanation
To find the marbles in each jar, divide the total marbles by the number of jars.
961/31 = 31
Problem 4
In a class, there are 961 students and 1 teacher. How many students are there per teacher?
There are 961 students per teacher.
Explanation
Dividing the students by the total teachers, we will get the number of students per teacher.
961/1 = 961
Problem 5
961 books need to be arranged in 31 shelves. How many books will go on each shelf?
Each of the shelves has 31 books.
Explanation
Divide total books by shelves.
961/31 = 31
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FAQs on Factors of 961
1.What are the factors of 961?
2.Mention the prime factor of 961.
3.Is 961 a perfect square?
4.Mention the factor pairs of 961?
5.What is the square root of 961?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 961?
7.What are some fun ways kids in Vietnam can practice Factors of 961 with numbers?
8.What role do numbers and Factors of 961 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 961 skills?
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Important Glossaries for Factor of 961
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 961 are 1, 31, and 961.
- Prime factor: The factor which is a prime number. For example, 31 is the prime factor of 961.
- 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 961 are (1, 961) and (31, 31).
- Perfect square: A number that can be expressed as the product of an integer with itself. For example, 961 is a perfect square because it is 31 × 31.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 961 is 31 × 31.
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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.
