101 LearnersLast updated on May 26th, 2025
Factors of 736
Factors are the numbers that divide any given number evenly without a 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 736, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 736?
The numbers that divide 736 evenly are known as factors of 736.
A factor of 736 is a number that divides the number without a remainder.
The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, and 736.
Negative factors of 736: -1, -2, -4, -8, -16, -23, -32, -46, -92, -184, -368, and -736.
Prime factors of 736: 2 and 23.
Prime factorization of 736: 24 × 23.
The sum of factors of 736: 1 + 2 + 4 + 8 + 16 + 23 + 32 + 46 + 92 + 184 + 368 + 736 = 1512
How to Find Factors of 736?
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 736. Identifying the numbers which are multiplied to get the number 736 is the multiplication method.
Step 1: Multiply 736 by 1, 736 × 1 = 736.
Step 2: Check for other numbers that give 736 after multiplying:
2 × 368 = 736
4 × 184 = 736
8 × 92 = 736
16 × 46 = 736
23 × 32 = 736
Therefore, the positive factor pairs of 736 are: (1, 736), (2, 368), (4, 184), (8, 92), (16, 46), (23, 32).
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 736 by 1, 736 ÷ 1 = 736.
Step 2: Continue dividing 736 by the numbers until the remainder becomes 0.
736 ÷ 1 = 736
736 ÷ 2 = 368
736 ÷ 4 = 184
736 ÷ 8 = 92
736 ÷ 16 = 46
736 ÷ 23 = 32
Therefore, the factors of 736 are: 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 736 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
736 ÷ 2 = 368
368 ÷ 2 = 184
184 ÷ 2 = 92
92 ÷ 2 = 46
46 ÷ 2 = 23
23 ÷ 23 = 1
The prime factors of 736 are 2 and 23.
The prime factorization of 736 is: 24 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 736 is divided by 2 to get 368.
Step 2: Now divide 368 by 2 to get 184.
Step 3: Then divide 184 by 2 to get 92.
Step 4: Divide 92 by 2 to get 46.
Step 5: Divide 46 by 2 to get 23. Here, 23 is a prime number and cannot be divided further.
So, the prime factorization of 736 is: 2^4 × 23.
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 736: (1, 736), (2, 368), (4, 184), (8, 92), (16, 46), and (23, 32).
Negative factor pairs of 736: (-1, -736), (-2, -368), (-4, -184), (-8, -92), (-16, -46), and (-23, -32).
Common Mistakes and How to Avoid Them in Factors of 736
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 number. Always remember to include 1 and the number itself.
For example, in factors of 736, 1 and 736 are also factors.
Factors of 736 Examples
Problem 1
There are 16 students and 736 pages. How will they divide it equally?
They will get 46 pages each.
Explanation
To divide the pages equally, we need to divide the total pages by the number of students.
736/16 = 46
Problem 2
A rectangular garden has a length of 46 meters and a total area of 736 square meters. Find the width.
16 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 736 = 46 × width
To find the value of width, we need to divide 736 by 46.
736/46 = width
Width = 16.
Problem 3
There are 32 boxes and 736 candies. How many candies will be in each box?
Each box will have 23 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
736/32 = 23
Problem 4
In a school, there are 92 students and 736 pencils. How many pencils are there for each student?
There are 8 pencils for each student.
Explanation
Dividing the pencils by the total number of students, we get the number of pencils for each student.
736/92 = 8
Problem 5
736 books need to be arranged in 23 shelves. How many books will go on each shelf?
Each shelf will have 32 books.
Explanation
Divide the total books by the shelves.
736/23 = 32
FAQs on Factors of 736
1.What are the factors of 736?
2.Mention the prime factors of 736.
3.Is 736 a multiple of 8?
4.Mention the factor pairs of 736?
5.What is the square of 736?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 736?
7.What are some fun ways kids in United Kingdom can practice Factors of 736 with numbers?
8.What role do numbers and Factors of 736 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 736 skills?
Important Glossaries for Factor of 736
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, and 736.
- Prime factors: The factors which are prime numbers. For example, 2 and 23 are prime factors of 736.
- 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 736 are (1, 736), (2, 368), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 736 is 24 × 23.
- Multiple: A number that can be divided by another number without a remainder. For example, 736 is a multiple of 8.
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About BrightChamps in United Kingdom
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.
