101 LearnersLast updated on May 26th, 2025
Factors of 749
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 749, how they are used in real life, and tips to learn them quickly.
What are the Factors of 749?
The numbers that divide 749 evenly are known as factors of 749.
A factor of 749 is a number that divides the number without remainder.
The factors of 749 are 1 and 749.
Negative factors of 749: -1 and -749.
Prime factorization of 749: 7 × 107.
The sum of factors of 749: 1 + 749 = 750
How to Find Factors of 749?
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 749. Identifying the numbers which are multiplied to get the number 749 is the multiplication method.
Step 1: Multiply 749 by 1, 749 × 1 = 749.
Step 2: Since 749 is a product of two prime numbers, there are no other whole number pairs that give 749.
Therefore, the positive factor pairs of 749 are: (1, 749).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 749 by 1, 749 ÷ 1 = 749.
Step 2: Check for division using other numbers until the remainder becomes 0.
Since 749 is a product of prime numbers 7 and 107, no other division results in a whole number.
Therefore, the factors of 749 are: 1 and 749.
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 749 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
749 ÷ 7 = 107 1
07 ÷ 107 = 1
The prime factors of 749 are 7 and 107.
The prime factorization of 749 is: 7 × 107.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: 749 is divided by 7 to get 107.
Step 2: Further divide 107 by 107 to get 1.
So, the prime factorization of 749 is: 7 × 107.
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 749: (1, 749).
Negative factor pairs of 749: (-1, -749).
Common Mistakes and How to Avoid Them in Factors of 749
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
People might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 749, 1 and 749 are also factors.
Factors of 749 Examples
Problem 1
There are 749 pages in a book. If each section has 1 page, how many sections are there?
There will be 749 sections.
Explanation
To divide the pages equally into sections, we need to divide the total pages by the number of pages per section.
749/1 = 749
Problem 2
A runner completes 749 meters in a single race. How many races would they need to run to complete 749 meters if each race is 1 meter?
They would need to run 749 races.
Explanation
To find out how many races at 1 meter each are needed to cover 749 meters:
749/1 = 749
Problem 3
There are 7 classes, and 749 students. How many students are in each class if they are distributed equally?
Each class will have 107 students.
Explanation
To find the number of students in each class, divide the total students by the number of classes.
749/7 = 107
Problem 4
A conference room can fit 749 chairs. If 1 chair is placed in each row, how many rows are there?
There are 749 rows.
Explanation
Dividing the total number of chairs by chairs per row gives the number of rows.
749/1 = 749
Problem 5
A single bus can carry 107 passengers. How many buses are needed to carry 749 passengers?
7 buses are needed.
Explanation
Divide the total number of passengers by the number of passengers per bus.
749/107 = 7
FAQs on Factors of 749
1.What are the factors of 749?
2.Mention the prime factors of 749.
3.Is 749 a multiple of 7?
4.Mention the factor pairs of 749?
5.Does 749 have any other factors?
6.How can children in India use numbers in everyday life to understand Factors of 749?
7.What are some fun ways kids in India can practice Factors of 749 with numbers?
8.What role do numbers and Factors of 749 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 749 skills?
Important Glossaries for Factors of 749
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 749 are 1 and 749.
- Prime factors: The factors which are prime numbers. For example, 7 and 107 are prime factors of 749.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pair of 749 is (1, 749).
- Prime factorization: The process of expressing a number as the product of its prime factors, such as 7 × 107 for 749.
- Product: The result of multiplying two numbers. For example, the product of 7 and 107 is 749.
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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.
