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Last updated on May 26th, 2025

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Factors of 1972

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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 1972, how they are used in real life, and the tips to learn them quickly.

Factors of 1972 for Qatari Students
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What are the Factors of 1972?

The numbers that divide 1972 evenly are known as factors of 1972.

 

A factor of 1972 is a number that divides the number without remainder.

 

The factors of 1972 are 1, 2, 4, 7, 14, 28, 71, 142, 284, 493, 986, and 1972.

 

Negative factors of 1972: -1, -2, -4, -7, -14, -28, -71, -142, -284, -493, -986, and -1972.

 

Prime factors of 1972: 2, 7, and 71.

 

Prime factorization of 1972: 2² × 7 × 71.

 

The sum of factors of 1972: 1 + 2 + 4 + 7 + 14 + 28 + 71 + 142 + 284 + 493 + 986 + 1972 = 4004

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How to Find Factors of 1972?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1972. Identifying the numbers which are multiplied to get the number 1972 is the multiplication method.

 

Step 1: Multiply 1972 by 1, 1972 × 1 = 1972.

 

Step 2: Check for other numbers that give 1972 after multiplying

 

2 × 986 = 1972

4 × 493 = 1972

7 × 284 = 1972

14 × 142 = 1972

28 × 71 = 1972

 

Therefore, the positive factor pairs of 1972 are: (1, 1972), (2, 986), (4, 493), (7, 284), (14, 142), (28, 71).

 

All these factor pairs result in 1972.

 

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 as whole numbers as factors. Factors can be calculated by following a simple division method

 

Step 1: Divide 1972 by 1, 1972 ÷ 1 = 1972.

 

Step 2: Continue dividing 1972 by the numbers until the remainder becomes 0.

 

1972 ÷ 1 = 1972

1972 ÷ 2 = 986

1972 ÷ 4 = 493

1972 ÷ 7 = 284

1972 ÷ 14 = 142

1972 ÷ 28 = 71

 

Therefore, the factors of 1972 are: 1, 2, 4, 7, 14, 28, 71, 142, 284, 493, 986, 1972.

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Prime Factors and Prime Factorization

The factors can be found by dividing it with a 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 1972 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

1972 ÷ 2 = 986

986 ÷ 2 = 493

493 ÷ 7 = 71

71 ÷ 71 = 1

 

The prime factors of 1972 are 2, 7, and 71.

 

The prime factorization of 1972 is: 2² × 7 × 71.

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Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows

 

Step 1: Firstly, 1972 is divided by 2 to get 986.

 

Step 2: Now divide 986 by 2 to get 493.

 

Step 3: Then divide 493 by 7 to get 71. Here, 71 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1972 is: 2² × 7 × 71.

 

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

 

Both positive and negative factors constitute factor pairs.

 

Positive factor pairs of 1972: (1, 1972), (2, 986), (4, 493), (7, 284), (14, 142), (28, 71).

 

Negative factor pairs of 1972: (-1, -1972), (-2, -986), (-4, -493), (-7, -284), (-14, -142), (-28, -71).

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Common Mistakes and How to Avoid Them in Factors of 1972

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

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Forgetting the number itself and 1 is a factor

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Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every word. Always remember to include 1 and the number itself.

 

For example, in factors of 1972, 1 and 1972 is also a factor.

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Factors of 1972 Examples

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Problem 1

There are 4 teams and 1972 participants. How will they be divided equally?

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Each team will have 493 participants.

Explanation

To divide the participants equally, we need to divide the total participants by the number of teams.

 

1972/4 = 493

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Problem 2

A garden has a rectangular shape with a length of 14 meters and a total area of 1972 square meters. Find the width.

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141 meters.

Explanation

To find the width of the garden, we use the formula,

 

Area = length × width

 

1972 = 14 × width

 

To find the value of width, we need to shift 14 to the left side.

 

1972/14 = width

 

Width = 141.

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Problem 3

There are 28 crates and 1972 apples. How many apples will be in each crate?

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Each crate will have 71 apples.

Explanation

To find the apples in each crate, divide the total apples by the number of crates.

 

1972/28 = 71

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Problem 4

In an auditorium, there are 1972 seats and 7 sections. How many seats are there in each section?

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There are 284 seats in each section.

Explanation

Dividing the total seats by the number of sections, we will get the number of seats in each section.

 

1972/7 = 284

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Problem 5

A library has 1972 books and 142 shelves. How many books will go on each shelf?

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Each of the shelves has 14 books.

Explanation

Divide the total books by the number of shelves.

 

1972/142 = 14

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FAQs on Factors of 1972

1.What are the factors of 1972?

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2.Mention the prime factors of 1972.

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3.Is 1972 a multiple of 4?

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4.Mention the factor pairs of 1972?

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5.What is the square of 1972?

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6.How can children in Qatar use numbers in everyday life to understand Factors of 1972?

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7.What are some fun ways kids in Qatar can practice Factors of 1972 with numbers?

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8.What role do numbers and Factors of 1972 play in helping children in Qatar develop problem-solving skills?

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9.How can families in Qatar create number-rich environments to improve Factors of 1972 skills?

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Important Glossaries for Factor of 1972

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1972 are 1, 2, 4, 7, 14, 28, 71, 142, 284, 493, 986, and 1972.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 7, and 71 are prime factors of 1972.
     
  • 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 1972 are (1, 1972), (2, 986), etc.
     
  • Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1972 is 2² × 7 × 71.
     
  • Multiple: A number that can be divided by another number without a remainder. For example, 1972 is a multiple of 4.
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About BrightChamps in Qatar

At BrightChamps, numbers are more than symbols—they open pathways to countless chances! Our mission is to help kids throughout Qatar master important math skills, focusing today on Factors of 1972 with special attention to factors—in an engaging, clear, and fun way. Whether your child is figuring out the speed of a ride at Angry Birds World, tracking local football scores, or managing their allowance for gadgets, strong number skills boost their confidence for daily tasks. Our interactive lessons make learning straightforward and enjoyable. Since kids in Qatar learn uniquely, we customize lessons to each child’s needs. From Doha’s modern cityscape to desert surroundings, BrightChamps brings math to life across Qatar. Let’s make factors an exciting part of every child’s math journey!
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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.

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Fun Fact

: She loves to read number jokes and games.

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