Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 31 students and 961 apples. How will they divide it equally?
They will get 31 apples each.
To divide the apples equally, we need to divide the total apples by the number of students.
961/31 = 31
A square garden has an area of 961 square meters. What is the length of one side?
31 meters.
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
There are 961 marbles and 31 jars. How many marbles will be in each jar?
Each jar will have 31 marbles.
To find the marbles in each jar, divide the total marbles by the number of jars.
961/31 = 31
In a class, there are 961 students and 1 teacher. How many students are there per teacher?
There are 961 students per teacher.
Dividing the students by the total teachers, we will get the number of students per teacher.
961/1 = 961
961 books need to be arranged in 31 shelves. How many books will go on each shelf?
Each of the shelves has 31 books.
Divide total books by shelves.
961/31 = 31
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.
: She loves to read number jokes and games.