Factors of 738
2026-02-28 17:18 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 738, how they are used in real life, and tips to learn them quickly.

What are the Factors of 738?

The numbers that divide 738 evenly are known as factors of 738.

A factor of 738 is a number that divides the number without remainder.

The factors of 738 are 1, 2, 3, 6, 123, 246, 369, and 738.

Negative factors of 738: -1, -2, -3, -6, -123, -246, -369, and -738.

Prime factors of 738: 2, 3, and 41.

Prime factorization of 738: 2 × 3 × 3 × 41.

The sum of factors of 738: 1 + 2 + 3 + 6 + 123 + 246 + 369 + 738 = 1488

How to Find Factors of 738?

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

  • Finding factors using multiplication
  • Finding factors using the 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 738. Identifying the numbers which are multiplied to get the number 738 is the multiplication method.

Step 1: Multiply 738 by 1, 738 × 1 = 738.

Step 2: Check for other numbers that give 738 after multiplying

2 × 369 = 738

3 × 246 = 738

6 × 123 = 738

Therefore, the positive factor pairs of 738 are: (1, 738), (2, 369), (3, 246), (6, 123).

All these factor pairs result in 738.

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 738 by 1, 738 ÷ 1 = 738.

Step 2: Continue dividing 738 by the numbers until the remainder becomes 0.

738 ÷ 1 = 738

738 ÷ 2 = 369

738 ÷ 3 = 246

738 ÷ 6 = 123

Therefore, the factors of 738 are: 1, 2, 3, 6, 123, 246, 369, and 738.

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

738 ÷ 2 = 369

369 ÷ 3 = 123

123 ÷ 3 = 41

41 ÷ 41 = 1

The prime factors of 738 are 2, 3, and 41.

The prime factorization of 738 is: 2 × 3 × 3 × 41.

Factor Tree

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

Step 1: Firstly, 738 is divided by 2 to get 369.

Step 2: Now divide 369 by 3 to get 123.

Step 3: Then divide 123 by 3 to get 41. Here, 41 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 738 is: 2 × 3 × 3 × 41.

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 738: (1, 738), (2, 369), (3, 246), (6, 123).

Negative factor pairs of 738: (-1, -738), (-2, -369), (-3, -246), (-6, -123).

Common Mistakes and How to Avoid Them in Factors of 738

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 369 apples, and each basket can hold 2 apples. How many baskets are needed?

Okay, lets begin

184 baskets are needed.

Explanation

To find how many baskets are needed, we divide the total apples by the number of apples each basket can hold.

369/2 = 184.5

Since we can't have half a basket, we round up to 185 baskets.

Well explained 👍

Problem 2

A rectangular floor has an area of 738 square meters and a width of 6 meters. What is the length of the floor?

Okay, lets begin

123 meters.

Explanation

To find the length of the floor, we use the formula, Area = length × width 738 = 6 × length

To find the value of length, we divide the area by the width.

738/6 = length

Length = 123.

Well explained 👍

Problem 3

A shipment contains 246 boxes, and each container can hold 3 boxes. How many containers are required?

Okay, lets begin

82 containers are required.

Explanation

To find the number of containers needed, divide the total boxes by the number of boxes each container holds.

246/3 = 82

Well explained 👍

Problem 4

In a school event, there are 738 chairs and 123 rows. How many chairs are in each row?

Okay, lets begin

6 chairs are in each row.

Explanation

Dividing the total chairs by the number of rows gives the number of chairs in each row.

738/123 = 6

Well explained 👍

Problem 5

A library has 369 books to be arranged equally on 3 shelves. How many books will go on each shelf?

Okay, lets begin

123 books will go on each shelf.

Explanation

Divide the total books by the number of shelves to find the number of books on each shelf.

369/3 = 123

Well explained 👍

FAQs on Factors of 738

1.What are the factors of 738?

1, 2, 3, 6, 123, 246, 369, and 738 are the factors of 738.

2.Mention the prime factors of 738.

The prime factors of 738 are 2, 3, and 41.

3.Is 738 a multiple of 3?

4.Mention the factor pairs of 738?

(1, 738), (2, 369), (3, 246), (6, 123) are the factor pairs of 738.

5.What is the square of 738?

Important Glossaries for Factors of 738

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 738 are 1, 2, 3, 6, 123, 246, 369, and 738.
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 41 are prime factors of 738.
  • 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 738 are (1, 738), (2, 369), etc.
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 738 is 2 × 3 × 3 × 41.
  • Negative factors: Factors of a number that are negative. For example, the negative factors of 738 are -1, -2, -3, -6, -123, -246, -369, and -738.

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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.