118 LearnersLast updated on May 26th, 2025
Factors of 1792
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 1792, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1792?
The numbers that divide 1792 evenly are known as factors of 1792.
A factor of 1792 is a number that divides the number without remainder.
The factors of 1792 are 1, 2, 4, 8, 16, 32, 56, 112, 224, 448, 896, and 1792.
Negative factors of 1792: -1, -2, -4, -8, -16, -32, -56, -112, -224, -448, -896, and -1792.
Prime factors of 1792: 2 and 7.
Prime factorization of 1792: 2^8 × 7.
The sum of factors of 1792: 1 + 2 + 4 + 8 + 16 + 32 + 56 + 112 + 224 + 448 + 896 + 1792 = 3591
How to Find Factors of 1792?
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 1792. Identifying the numbers which are multiplied to get the number 1792 is the multiplication method. Step 1: Multiply 1792 by 1, 1792 × 1 = 1792. Step 2: Check for other numbers that give 1792 after multiplying 2 × 896 = 1792 4 × 448 = 1792 8 × 224 = 1792 16 × 112 = 1792 32 × 56 = 1792 Therefore, the positive factor pairs of 1792 are: (1, 1792), (2, 896), (4, 448), (8, 224), (16, 112), (32, 56). 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 1792 by 1, 1792 ÷ 1 = 1792.
Step 2: Continue dividing 1792 by the numbers until the remainder becomes 0.
1792 ÷ 1 = 1792
1792 ÷ 2 = 896
1792 ÷ 4 = 448
1792 ÷ 8 = 224
1792 ÷ 16 = 112
1792 ÷ 32 = 56
Therefore, the factors of 1792 are: 1, 2, 4, 8, 16, 32, 56, 112, 224, 448, 896, 1792.
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 1792 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1792 ÷ 2 = 896
896 ÷ 2 = 448
448 ÷ 2 = 224
224 ÷ 2 = 112
112 ÷ 2 = 56
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
The prime factors of 1792 are 2 and 7.
The prime factorization of 1792 is: 2^8 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1792 is divided by 2 to get 896.
Step 2: Now divide 896 by 2 to get 448.
Step 3: Then divide 448 by 2 to get 224.
Step 4: Divide 224 by 2 to get 112.
Step 5: Divide 112 by 2 to get 56.
Step 6: Divide 56 by 2 to get 28.
Step 7: Divide 28 by 2 to get 14.
Step 8: Divide 14 by 2 to get 7.
Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1792 is: 2^8 × 7.
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 1792: (1, 1792), (2, 896), (4, 448), (8, 224), (16, 112), and (32, 56).
Negative factor pairs of 1792: (-1, -1792), (-2, -896), (-4, -448), (-8, -224), (-16, -112), and (-32, -56).
Common Mistakes and How to Avoid Them in Factors of 1792
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 1792, 1 and 1792 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1792 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1792/1.5 = 1194.666..., and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of 1792 are prime numbers.
For example, 2 and 7 are the prime factors of 1792, but it has other factors like 56, 112.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1792 as 2^8 × 7 and missing all the key factors.
Factors of 1792 Examples
Problem 1
There are 56 marbles and 1792 candies. How will they distribute them equally?
They will get 32 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of marbles.
1792/56 = 32
Problem 2
A rectangular garden has a length of 112 meters and a total area of 1792 square meters. Find the width.
16 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1792 = 112 × width
To find the value of width,we need to shift 112 to the left side.
1792/112 = width
Width = 16.
Problem 3
There are 112 baskets and 1792 apples. How many apples will be in each basket?
Each basket will have 16 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1792/112 = 16
Problem 4
In a class, there are 1792 students, and 56 groups. How many students are there in each group?
There are 32 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1792/56 = 32
Problem 5
1792 chairs need to be arranged in 112 rows. How many chairs will go in each row?
Each row will have 16 chairs.
Explanation
Divide total chairs by rows.
1792/112 = 16
FAQs on Factors of 1792
1.What are the factors of 1792?
2.Mention the prime factors of 1792.
3.Is 1792 a multiple of 32?
4.Mention the factor pairs of 1792?
5.What is the square of 1792?
6.How can children in Canada use numbers in everyday life to understand Factors of 1792?
7.What are some fun ways kids in Canada can practice Factors of 1792 with numbers?
8.What role do numbers and Factors of 1792 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1792 skills?
Important Glossaries for Factor of 1792
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1792 are 1, 2, 4, 8, 16, 32, 56, 112, 224, 448, 896, and 1792.
- Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 1792.
- 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 1792 are (1, 1792), (2, 896), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1792 is 2^8 × 7.
- Multiple: A number that can be divided by another number without a remainder. For instance, 1792 is a multiple of 56.
Explore More numbers
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.
