106 LearnersLast updated on May 26th, 2025
Factors of 748
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
- 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 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.
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
- Using factor tree
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.
Mistake 1
Forgetting the number itself and 1 is a factor
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 748, 1 and 748 are also factors.
Factors of 748 Examples
Problem 1
There are 748 apples, and 4 baskets. How many apples will go into each basket if divided equally?
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
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.
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.
Problem 3
A library has 748 books and 68 shelves. How many books will be on each shelf if arranged equally?
Each shelf will have 11 books.
Explanation
To find the books on each shelf, divide the total books by the shelves. 748/68 = 11
Problem 4
A community center has 748 chairs and 11 rooms. How many chairs will go into each room if divided equally?
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
Problem 5
748 candies need to be shared among 34 children. How many candies will each child receive?
Each child will receive 22 candies.
Explanation
Divide total candies by the number of children.
748/34 = 22
FAQs on Factors of 748
1.What are the factors of 748?
2.Mention the prime factors of 748.
3.Is 748 a multiple of 17?
4.Mention the factor pairs of 748?
5.What is the square of 748?
6.How can children in India use numbers in everyday life to understand Factors of 748?
7.What are some fun ways kids in India can practice Factors of 748 with numbers?
8.What role do numbers and Factors of 748 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 748 skills?
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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About BrightChamps in India
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.
