Factors of 1372
2026-02-28 23:15 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 1372, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1372?

The numbers that divide 1372 evenly are known as factors of 1372.

A factor of 1372 is a number that divides the number without remainder.

The factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372.

Negative factors of 1372: -1, -2, -4, -7, -14, -28, -49, -98, -196, -343, -686, and -1372.

Prime factors of 1372: 2 and 7.

Prime factorization of 1372: 2² × 7³.

The sum of factors of 1372: 1 + 2 + 4 + 7 + 14 + 28 + 49 + 98 + 196 + 343 + 686 + 1372 = 2800

How to Find Factors of 1372?

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

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1372. Identifying the numbers which are multiplied to get the number 1372 is the multiplication method.

Step 1: Multiply 1372 by 1, 1372 × 1 = 1372.

Step 2: Check for other numbers that give 1372 after multiplying

2 × 686 = 1372

4 × 343 = 1372

7 × 196 = 1372

14 × 98 = 1372

28 × 49 = 1372

Therefore, the positive factor pairs of 1372 are: (1, 1372), (2, 686), (4, 343), (7, 196), (14, 98), (28, 49).

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 1372 by 1, 1372 ÷ 1 = 1372.

Step 2: Continue dividing 1372 by the numbers until the remainder becomes 0.

1372 ÷ 1 = 1372

1372 ÷ 2 = 686

1372 ÷ 4 = 343

1372 ÷ 7 = 196

1372 ÷ 14 = 98

1372 ÷ 28 = 49

Therefore, the factors of 1372 are: 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372.

Prime Factors and Prime Factorization

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 1372 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1372 ÷ 2 = 686

686 ÷ 2 = 343

343 ÷ 7 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

The prime factors of 1372 are 2 and 7.

The prime factorization of 1372 is: 2² × 7³.

Factor Tree

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

Step 1: Firstly, 1372 is divided by 2 to get 686.

Step 2: Now divide 686 by 2 to get 343.

Step 3: Then divide 343 by 7 to get 49.

Step 4: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1372 is: 2² × 7³.

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 1372: (1, 1372), (2, 686), (4, 343), (7, 196), (14, 98), (28, 49).

Negative factor pairs of 1372: (-1, -1372), (-2, -686), (-4, -343), (-7, -196), (-14, -98), (-28, -49).

Common Mistakes and How to Avoid Them in Factors of 1372

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 14 participants and 1372 prizes. How will they divide the prizes equally?

Okay, lets begin

They will get 98 prizes each.

Explanation

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

1372/14 = 98

Well explained 👍

Problem 2

A garden is rectangular, with a length of 49 meters and a total area of 1372 square meters. Find the width.

Okay, lets begin

28 meters.

Explanation

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

Area = length × width

1372 = 49 × width

To find the value of width, we need to shift 49 to the left side.

1372/49 = width

Width = 28.

Well explained 👍

Problem 3

There are 28 bins and 1372 pieces of trash. How many pieces will be in each bin?

Okay, lets begin

Each bin will have 49 pieces.

Explanation

To find the pieces in each bin, divide the total pieces by the number of bins.

1372/28 = 49

Well explained 👍

Problem 4

In a workshop, there are 98 participants, and 14 teams. How many participants are there in each team?

Okay, lets begin

There are 7 participants in each team.

Explanation

Dividing the participants by the total teams, we will get the number of participants in each team.

98/14 = 7

Well explained 👍

Problem 5

1372 apples need to be packed in 49 boxes. How many apples will go in each box?

Okay, lets begin

Each of the boxes will have 28 apples.

Explanation

Divide total apples by boxes.

1372/49 = 28

Well explained 👍

FAQs on Factors of 1372

1.What are the factors of 1372?

1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372 are the factors of 1372.

2.Mention the prime factors of 1372.

The prime factors of 1372 are 2² × 7³.

3.Is 1372 a multiple of 7?

4.Mention the factor pairs of 1372?

(1, 1372), (2, 686), (4, 343), (7, 196), (14, 98), (28, 49) are the factor pairs of 1372.

5.What is the square of 1372?

The square of 1372 is 1883584.

Important Glossaries for Factors of 1372

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372.
     
  • Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 1372.
     
  • 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 1372 are (1, 1372), (2, 686), etc.
     
  • Prime factorization: Breaking down a number into the multiplication of its prime factors. For example, the prime factorization of 1372 is 2² × 7³.
     
  • Multiples: Numbers that can be divided by another number without a remainder. For example, 1372 is a multiple of 7.

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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.