Factors of 748
2026-02-28 23:29 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 748, how they are used in real life, and tips to learn them quickly.

What are the Factors of 748?

The numbers that divide 748 evenly are known as factors of 748.

A factor of 748 is a number that divides the number without remainder.

The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, and 748.

Negative factors of 748: -1, -2, -4, -11, -17, -22, -34, -44, -68, -187, -374, and -748.

Prime factors of 748: 2, 11, and 17.

Prime factorization of 748: 2² × 11 × 17.

The sum of factors of 748: 1 + 2 + 4 + 11 + 17 + 22 + 34 + 44 + 68 + 187 + 374 + 748 = 1512

How to Find Factors of 748?

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 748. Identifying the numbers which are multiplied to get the number 748 is the multiplication method.

Step 1: Multiply 748 by 1, 748 × 1 = 748.

Step 2: Check for other numbers that give 748 after multiplying

2 × 374 = 748

4 × 187 = 748

11 × 68 = 748

17 × 44 = 748

Therefore, the positive factor pairs of 748 are: (1, 748), (2, 374), (4, 187), (11, 68), (17, 44).

All these factor pairs result in 748.

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 748 by 1, 748 ÷ 1 = 748.

Step 2: Continue dividing 748 by the numbers until the remainder becomes 0.

748 ÷ 1 = 748

748 ÷ 2 = 374

748 ÷ 4 = 187

748 ÷ 11 = 68

748 ÷ 17 = 44

Therefore, the factors of 748 are: 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748.

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

748 ÷ 2 = 374

374 ÷ 2 = 187

187 ÷ 11 = 17

17 ÷ 17 = 1

The prime factors of 748 are 2, 11, and 17.

The prime factorization of 748 is: 2² × 11 × 17.

Factor Tree

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

Step 1: Firstly, 748 is divided by 2 to get 374.

Step 2: Now divide 374 by 2 to get 187.

Step 3: Then divide 187 by 11 to get 17.

Here, 17 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 748 is: 2² × 11 × 17.

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 748: (1, 748), (2, 374), (4, 187), (11, 68), and (17, 44).

Negative factor pairs of 748: (-1, -748), (-2, -374), (-4, -187), (-11, -68), and (-17, -44).

Common Mistakes and How to Avoid Them in Factors of 748

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 748 apples, and 4 baskets. How many apples will go into each basket if divided equally?

Okay, lets begin

Each basket will have 187 apples.

Explanation

To divide the apples equally, we need to divide the total apples by the number of baskets.

748/4 = 187

Well explained 👍

Problem 2

A rectangular garden has a total area of 748 square meters and a width of 17 meters. Find the length of the garden.

Okay, lets begin

44 meters.

Explanation

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

Area = length × width

748 = length × 17

To find the value of the length, we need to shift 17 to the left side.

748/17 = length

Length = 44.

Well explained 👍

Problem 3

A library has 748 books and 68 shelves. How many books will be on each shelf if arranged equally?

Okay, lets begin

Each shelf will have 11 books.

Explanation

To find the books on each shelf, divide the total books by the shelves. 748/68 = 11

Well explained 👍

Problem 4

A community center has 748 chairs and 11 rooms. How many chairs will go into each room if divided equally?

Okay, lets begin

Each room will have 68 chairs.

Explanation

Dividing the chairs by the total rooms, we will get the number of chairs in each room.

748/11 = 68

Well explained 👍

Problem 5

748 candies need to be shared among 34 children. How many candies will each child receive?

Okay, lets begin

Each child will receive 22 candies.

Explanation

Divide total candies by the number of children.

748/34 = 22

Well explained 👍

FAQs on Factors of 748

1.What are the factors of 748?

1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748 are the factors of 748.

2.Mention the prime factors of 748.

The prime factors of 748 are 2² × 11 × 17.

3.Is 748 a multiple of 17?

4.Mention the factor pairs of 748?

(1, 748), (2, 374), (4, 187), (11, 68), and (17, 44) are the factor pairs of 748.

5.What is the square of 748?

Important Glossaries for Factor of 748

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, and 748.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 11, and 17 are prime factors of 748.
     
  • 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 748 are (1, 748), (2, 374), etc.
     
  • Prime factorization: Breaking down a number into its prime factors. The prime factorization of 748 is 2² × 11 × 17.
     
  • Multiple: A multiple of a number is the product of that number and an integer. For example, 748 is a multiple of 17.

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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.