Factors of 971
2026-02-28 08:31 Diff
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Last updated on December 12, 2025

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 971, how they are used in real life, and tips to learn them quickly.

What are the Factors of 971?

The numbers that divide 971 evenly are known as factors of 971.

A factor of 971 is a number that divides the number without remainder.

The factors of 971 are 1 and 971.

Negative factors of 971: -1 and -971.

Prime factors of 971: 971 (since 971 is a prime number).

Prime factorization of 971: 971.

The sum of factors of 971: 1 + 971 = 972

How to Find Factors of 971?

Factors can be found using different methods. Mentioned below are some commonly used methods:

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 971. Identifying the numbers which are multiplied to get the number 971 is the multiplication method. Since 971 is a prime number, its only multiplication pair is:

Step 1: Multiply 971 by 1, 971 × 1 = 971.

Therefore, the only positive factor pair of 971 is: (1, 971).

For every positive factor, there is a negative factor.

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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 in whole numbers as factors. Factors can be calculated by following the simple division method -

Step 1: Divide 971 by 1, 971 ÷ 1 = 971.

Step 2: Check divisibility by other numbers.

Since 971 is a prime number, only 1 and 971 divide it without leaving a remainder.

Therefore, the factors of 971 are: 1 and 971.

Prime Factors and Prime Factorization

The factors can be found by dividing it with prime numbers. Since 971 is a prime number, its only prime factor is itself.

Using Prime Factorization: In this process, since 971 is prime, it can't be broken down further into other prime factors.

The prime factorization of 971 is: 971.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. For a prime number like 971, the factor tree is simple:

Step 1: Start with 971, which is already a prime number.

The prime factorization of 971 is: 971.

Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.

Positive factor pair of 971: (1, 971).

Negative factor pair of 971: (-1, -971).

Common Mistakes and How to Avoid Them in Factors of 971

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 971 apples and 1 basket. How will they be arranged?

Okay, lets begin

All 971 apples will be in the one basket.

Explanation

To find how apples will be arranged, since there is only one basket, all 971 apples will go into that basket.

Well explained 👍

Problem 2

A parade has 971 participants and each row has 1 participant. How many rows are there?

Okay, lets begin

There are 971 rows.

Explanation

To find the number of rows, since each row has 1 participant:

971/1 = 971

Well explained 👍

Problem 3

A marathon has 971 runners with each runner having their own lane. How many lanes are there?

Okay, lets begin

There are 971 lanes.

Explanation

Since each runner has their own lane, the number of lanes is equal to the number of runners:

971/1 = 971

Well explained 👍

Problem 4

A farmer has 971 cages and each cage holds one rabbit. How many rabbits does the farmer have?

Okay, lets begin

The farmer has 971 rabbits.

Explanation

Since each cage holds one rabbit, the number of cages is equal to the number of rabbits:

971/1 = 971

Well explained 👍

Problem 5

971 students need to be seated in an auditorium with 1 seat per student. How many seats are needed?

Okay, lets begin

971 seats are needed.

Explanation

Since each student requires one seat, the number of students equals the number of seats needed:

971/1 = 971

Well explained 👍

FAQs on Factors of 971

1.What are the factors of 971?

1 and 971 are the factors of 971.

2.Mention the prime factors of 971.

The prime factor of 971 is 971.

3.Is 971 a multiple of 1?

4.Mention the factor pairs of 971?

(1, 971) is the factor pair of 971.

5.Is 971 a prime number?

Yes, 971 is a prime number.

Important Glossaries for Factors of 971

  • Factors: Numbers that divide the given number without leaving a remainder. For example, the factors of 971 are 1 and 971.
  • Prime number: A number that has exactly two distinct positive divisors: 1 and itself. For example, 971 is a prime number.
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number. For example, the factor pair of 971 is (1, 971).
  • Divisibility: The ability of one number to be divided by another without a remainder. For example, 971 is divisible by 1.
  • Multiplication: The process of combining two numbers to get a product. For example, 1 multiplied by 971 gives 971.

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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.