123 LearnersLast updated on May 26th, 2025
Factors of 782
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 782, how they are used in real life, and tips to learn them quickly.
What are the Factors of 782?
The numbers that divide 782 evenly are known as factors of 782.
A factor of 782 is a number that divides the number without a remainder.
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, and 782.
Negative factors of 782: -1, -2, -17, -23, -34, -46, -391, and -782.
Prime factors of 782: 2, 17, and 23.
Prime factorization of 782: 2 × 17 × 23.
The sum of factors of 782: 1 + 2 + 17 + 23 + 34 + 46 + 391 + 782 = 1296
How to Find Factors of 782?
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 782. Identifying the numbers which are multiplied to get the number 782 is the multiplication method.
Step 1: Multiply 782 by 1, 782 × 1 = 782.
Step 2: Check for other numbers that give 782 after multiplying
2 × 391 = 782
17 × 46 = 782
23 × 34 = 782
Therefore, the positive factor pairs of 782 are: (1, 782), (2, 391), (17, 46), (23, 34).
All these factor pairs result in 782.
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 the simple division method
Step 1: Divide 782 by 1, 782 ÷ 1 = 782.
Step 2: Continue dividing 782 by the numbers until the remainder becomes 0.
782 ÷ 1 = 782
782 ÷ 2 = 391
782 ÷ 17 = 46
782 ÷ 23 = 34
Therefore, the factors of 782 are: 1, 2, 17, 23, 34, 46, 391, 782.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 782 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
782 ÷ 2 = 391
391 ÷ 17 = 23
23 ÷ 23 = 1
The prime factors of 782 are 2, 17, and 23.
The prime factorization of 782 is: 2 × 17 × 23.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 782 is divided by 2 to get 391.
Step 2: Now divide 391 by 17 to get 23.
Step 3: Here, 23 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 782 is: 2 × 17 × 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 782: (1, 782), (2, 391), (17, 46), (23, 34).
Negative factor pairs of 782: (-1, -782), (-2, -391), (-17, -46), (-23, -34).
Common Mistakes and How to Avoid Them in Factors of 782
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 782, 1 and 782 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 782 consist of -1, -2, -17, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 782/1.5 = 521.333, 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 782 are prime numbers.
For example, 2, 17, and 23 are the prime factors of 782, but it has other factors like 34 and 46.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 782 as 2 × 17 × 23 and missing all the key factors.
Factors of 782 Examples
Problem 1
There are 782 candies and 2 baskets. How will they divide them equally?
They will get 391 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of baskets.
782/2 = 391
Problem 2
A field is rectangular, the length of the field is 17 meters, and the total area is 782 square meters. Find the width.
46 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
782 = 17 × width
To find the value of width, we need to shift 17 to the left side.
782/17 = width
Width = 46.
Problem 3
There are 34 bags and 782 marbles. How many marbles will be in each bag?
Each bag will have 23 marbles.
Explanation
To find the marbles in each bag, divide the total marbles with the bags.
782/34 = 23
Problem 4
In a class, there are 782 students, and 46 groups. How many students are there in each group?
There are 17 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
782/46 = 17
Problem 5
782 pages need to be arranged in 23 binders. How many pages will go in each binder?
Each of the binders has 34 pages.
Explanation
Divide total pages with binders.
782/23 = 34
FAQs on Factors of 782
1.What are the factors of 782?
2.Mention the prime factors of 782.
3.Is 782 a multiple of 17?
4.Mention the factor pairs of 782?
5.What is the square of 782?
6.How can children in United States use numbers in everyday life to understand Factors of 782?
7.What are some fun ways kids in United States can practice Factors of 782 with numbers?
8.What role do numbers and Factors of 782 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 782 skills?
Important Glossaries for Factors of 782
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 782 are 1, 2, 17, 23, 34, 46, 391, and 782.
- Prime factors: The factors which are prime numbers. For example, 2, 17, and 23 are prime factors of 782.
- 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 782 are (1, 782), (2, 391), etc.
- Prime factorization: The process of writing a number as a product of its prime factors. For example, the prime factorization of 782 is 2 × 17 × 23.
- Negative factors: Factors that are negative numbers but still divide the original number without a remainder. For example, -1, -2, -17, etc., are negative factors of 782.
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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.
