Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 1971, how they are used in real life, and tips to learn them quickly.
The numbers that divide 1971 evenly are known as factors of 1971.
A factor of 1971 is a number that divides the number without a remainder.
The factors of 1971 are 1, 3, 657, and 1971.
Negative factors of 1971: -1, -3, -657, and -1971.
Prime factors of 1971: 3 and 657.
Prime factorization of 1971: 3 × 657.
The sum of factors of 1971: 1 + 3 + 657 + 1971 = 2632
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 1971. Identifying the numbers which are multiplied to get the number 1971 is the multiplication method.
Step 1: Multiply 1971 by 1, 1971 × 1 = 1971.
Step 2: Check for other numbers that give 1971 after multiplying
3 × 657 = 1971
Therefore, the positive factor pairs of 1971 are: (1, 1971) and (3, 657).
For every positive factor, there is a negative factor.
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 1971 by 1, 1971 ÷ 1 = 1971.
Step 2: Continue dividing 1971 by the numbers until the remainder becomes 0.
1971 ÷ 1 = 1971
1971 ÷ 3 = 657
Therefore, the factors of 1971 are: 1, 3, 657, and 1971.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 1971 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1971 ÷ 3 = 657
657 ÷ 657 = 1
The prime factors of 1971 are 3 and 657.
The prime factorization of 1971 is: 3 × 657.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1971 is divided by 3 to get 657. Here, 657 is not a prime number, but since it is a larger component of the factorization, it is left as is. So, the prime factorization of 1971 is: 3 × 657.
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 1971: (1, 1971) and (3, 657).
Negative factor pairs of 1971: (-1, -1971) and (-3, -657).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A company has 3 departments and 1971 employees. How many employees are in each department if they are divided equally?
Each department will have 657 employees.
To divide the employees equally, we need to divide the total employees by the number of departments.
1971/3 = 657
A rectangular field has a length of 3 meters and a total area of 1971 square meters. What is the width?
657 meters.
To find the width of the field, we use the formula,
Area = length × width
1971 = 3 × width
To find the value of width, we need to shift 3 to the left side.
1971/3 = width
Width = 657.
There are 657 boxes and 1971 items. How many items will be in each box?
Each box will have 3 items.
To find the items in each box, divide the total items by the number of boxes.
1971/657 = 3
A school has 1971 students and 3 different grades. How many students are there in each grade?
There are 657 students in each grade.
Dividing the students by the total grades, we will get the number of students in each grade.
1971/3 = 657
1971 books need to be arranged in 3 sections. How many books will go in each section?
Each section will have 657 books.
Divide the total books by the sections.
1971/3 = 657
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.