Factors of 248
2026-02-28 17:24 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 248, how they are used in real life, and tips to learn them quickly.

What are the Factors of 248?

The numbers that divide 248 evenly are known as factors of 248.

A factor of 248 is a number that divides the number without a remainder.

The factors of 248 are 1, 2, 4, 8, 31, 62, 124, and 248.

Negative factors of 248: -1, -2, -4, -8, -31, -62, -124, and -248.

Prime factors of 248: 2 and 31.

Prime factorization of 248: 2³ × 31.

The sum of factors of 248: 1 + 2 + 4 + 8 + 31 + 62 + 124 + 248 = 480

How to Find Factors of 248?

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 248. Identifying the numbers which are multiplied to get the number 248 is the multiplication method.

Step 1: Multiply 248 by 1, 248 × 1 = 248.

Step 2: Check for other numbers that give 248 after multiplying

2 × 124 = 248

4 × 62 = 248

8 × 31 = 248

Therefore, the positive factor pairs of 248 are: (1, 248), (2, 124), (4, 62), (8, 31).

All these factor pairs result in 248. 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 248 by 1, 248 ÷ 1 = 248.

Step 2: Continue dividing 248 by the numbers until the remainder becomes 0.

248 ÷ 1 = 248

248 ÷ 2 = 124

248 ÷ 4 = 62

248 ÷ 8 = 31

Therefore, the factors of 248 are: 1, 2, 4, 8, 31, 62, 124, 248.

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

248 ÷ 2 = 124

124 ÷ 2 = 62

62 ÷ 2 = 31

31 ÷ 31 = 1

The prime factors of 248 are 2 and 31.

The prime factorization of 248 is: 2³ × 31.

Factor Tree

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

Step 1: Firstly, 248 is divided by 2 to get 124.

Step 2: Now divide 124 by 2 to get 62.

Step 3: Then divide 62 by 2 to get 31.

Here, 31 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 248 is: 2³ × 31.

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 248: (1, 248), (2, 124), (4, 62), and (8, 31).

Negative factor pairs of 248: (-1, -248), (-2, -124), (-4, -62), and (-8, -31).

Common Mistakes and How to Avoid Them in Factors of 248

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 4 friends and 248 marbles. How will they divide it equally?

Okay, lets begin

They will get 62 marbles each.

Explanation

To divide the marbles equally, we need to divide the total marbles by the number of friends.

248/4 = 62

Well explained 👍

Problem 2

A field is rectangular, the length of the field is 31 meters and the total area is 248 square meters. Find the width?

Okay, lets begin

8 meters.

Explanation

To find the width of the field, we use the formula, Area = length × width

248 = 31 × width

To find the value of width, we need to shift 31 to the left side.

248/31 = width

Width = 8.

Well explained 👍

Problem 3

There are 8 bags and 248 candies. How many candies will be in each bag?

Okay, lets begin

Each bag will have 31 candies.

Explanation

To find the candies in each bag, divide the total candies by the bags.

248/8 = 31

Well explained 👍

Problem 4

In a class, there are 248 students, and 62 groups. How many students are there in each group?

Okay, lets begin

There are 4 students in each group.

Explanation

Dividing the students by the total groups, we will get the number of students in each group.

248/62 = 4

Well explained 👍

Problem 5

248 books need to be arranged in 8 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 31 books.

Explanation

Divide total books by shelves.

248/8 = 31

Well explained 👍

FAQs on Factors of 248

1.What are the factors of 248?

1, 2, 4, 8, 31, 62, 124, 248 are the factors of 248.

2.Mention the prime factors of 248.

The prime factors of 248 are 2³ × 31.

3.Is 248 a multiple of 8?

4.Mention the factor pairs of 248?

(1, 248), (2, 124), (4, 62), and (8, 31) are the factor pairs of 248.

5.What is the square of 248?

Important Glossaries for Factors of 248

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 248 are 1, 2, 4, 8, 31, 62, 124, and 248.
  • Prime factors: The factors which are prime numbers. For example, 2 and 31 are prime factors of 248.
  • 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 248 are (1, 248), (2, 124), etc.
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 248 is 2³ × 31.
  • Multiple: A number that can be divided by another number without a remainder. For example, 248 is a multiple of 8.

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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.