100 LearnersLast updated on May 26th, 2025
Factors of 7744
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 7744, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 7744?
The numbers that divide 7744 evenly are known as factors of 7744.
A factor of 7744 is a number that divides the number without remainder.
The factors of 7744 are 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 664, 1328, 1936, 3872, and 7744.
Negative factors of 7744: -1, -2, -4, -8, -16, -32, -53, -106, -212, -424, -664, -1328, -1936, -3872, and -7744.
Prime factors of 7744: 2 and 53.
Prime factorization of 7744: 24 × 532.
The sum of factors of 7744: 1 + 2 + 4 + 8 + 16 + 32 + 53 + 106 + 212 + 424 + 664 + 1328 + 1936 + 3872 + 7744 = 16408
How to Find Factors of 7744?
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 7744. Identifying the numbers which are multiplied to get the number 7744 is the multiplication method.
Step 1: Multiply 7744 by 1, 7744 × 1 = 7744.
Step 2: Check for other numbers that give 7744 after multiplying
2 × 3872 = 7744
4 × 1936 = 7744
8 × 968 = 7744
16 × 484 = 7744
32 × 242 = 7744
53 × 146 = 7744
106 × 73 = 7744
Therefore, the positive factor pairs of 7744 are: (1, 7744), (2, 3872), (4, 1936), (8, 968), (16, 484), (32, 242), (53, 146), and (106, 73).
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 7744 by 1, 7744 ÷ 1 = 7744.
Step 2: Continue dividing 7744 by the numbers until the remainder becomes 0.
7744 ÷ 1 = 7744
7744 ÷ 2 = 3872
7744 ÷ 4 = 1936
7744 ÷ 8 = 968
7744 ÷ 16 = 484
7744 ÷ 32 = 242
7744 ÷ 53 = 146
7744 ÷ 106 = 73
Therefore, the factors of 7744 are: 1, 2, 4, 8, 16, 32, 53, 106, 146, 212, 424, 664, 1328, 1936, 3872, and 7744.
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 7744 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
7744 ÷ 2 = 3872
3872 ÷ 2 = 1936
1936 ÷ 2 = 968
968 ÷ 2 = 484
484 ÷ 53 = 9.132 (not divisible)
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 7744 is divided by 2 to get 3872.
Step 2: Now divide 3872 by 2 to get 1936.
Step 3: Then divide 1936 by 2 to get 968.
Step 4: Divide 968 by 2 to get 484.
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 7744: (1, 7744), (2, 3872), (4, 1936), (8, 968), (16, 484), (32, 242), (53, 146), and (106, 73).
Negative factor pairs of 7744: (-1, -7744), (-2, -3872), (-4, -1936), (-8, -968), (-16, -484), (-32, -242), (-53, -146), and (-106, -73).
Common Mistakes and How to Avoid Them in Factors of 7744
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 7744, 1 and 7744 is also a factor.
Factors of 7744 Examples
Problem 1
There are 15 tables and 7744 chairs. How will they arrange it equally?
They will arrange 516 chairs on each table.
Explanation
To arrange the chairs equally, we need to divide the total chairs by the number of tables.
7744/15 = 516
Problem 2
A community garden is rectangular, the length of the garden is 32 meters and the total area is 7744 square meters. Find the width?
242 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
7744 = 32 × width
To find the value of width, we need to shift 32 to the left side.
7744/32 = width
Width = 242.
Problem 3
There are 53 boxes and 7744 chocolates. How many chocolates will be in each box?
Each box will have 146 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates by the boxes.
7744/53 = 146
Problem 4
In a laboratory, there are 7744 samples and 106 groups. How many samples are there in each group?
There are 73 samples in each group.
Explanation
Dividing the samples by the total groups, we will get the number of samples in each group.
7744/106 = 73
Problem 5
7744 seedlings need to be planted in 8 rows. How many seedlings will go in each row?
Each of the rows has 968 seedlings.
Explanation
Divide total seedlings by rows.
7744/8 = 968
FAQs on Factors of 7744
1.What are the factors of 7744?
2.Mention the prime factors of 7744.
3.Is 7744, a multiple of 32?
4.Mention the factor pairs of 7744?
5.What is the square root of 7744?
6.How can children in Canada use numbers in everyday life to understand Factors of 7744?
7.What are some fun ways kids in Canada can practice Factors of 7744 with numbers?
8.What role do numbers and Factors of 7744 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 7744 skills?
Important Glossaries for Factor of 7744
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7744 are 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 664, 1328, 1936, 3872, and 7744.
- Prime factors: The factors which are prime numbers. For example, 2 and 53 are prime factors of 7744.
- Prime Factorization: Breaking down a number into its prime factors. For example, the prime factorization of 7744 is 24 × 532.
- 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 7744 are (1, 7744), (2, 3872), etc.
- Square root: A number that produces a specified quantity when multiplied by itself. For example, the square root of 7744 is 88.
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About BrightChamps in Canada
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.
