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215 LearnersLast updated on December 17, 2025
Factors of 882
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 882, how they are used in real life, and tips to learn them quickly.
What are the Factors of 882?
The numbers that divide 882 evenly are known as factors of 882.
A factor of 882 is a number that divides the number without a remainder.
The factors of 882 are 1, 2, 3, 6, 9, 18, 21, 42, 49, 98, 147, 294, 441, and 882.
Negative factors of 882: -1, -2, -3, -6, -9, -18, -21, -42, -49, -98, -147, -294, -441, and -882.
Prime factors of 882: 2, 3, and 7.
Prime factorization of 882: 2 × 32 × 72.
The sum of factors of 882: 1 + 2 + 3 + 6 + 9 + 18 + 21 + 42 + 49 + 98 + 147 + 294 + 441 + 882 = 2013
| Factor Type | Values |
| Positive Factors of 36 | (1, 2, 3, 6, 9, 18, 21, 42, 49, 98, 147, 294, 441, 882) |
| Negative Factors of 36 | ( -1, -2, -3, -6, -9, -18, -21, -42, -49, -98, -147, -294, -441, -882) |
| Prime Factors of 36 | (2, 3, 7) |
| Prime Factorization of 36 | 2 × 32 × 72 |
| Sum of factors of 36 | 2013 |
How to Find Factors of 882?
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 882. Identifying the numbers that are multiplied to get the number 882 is the multiplication method.
Step 1: Multiply 882 by 1, 882 × 1 = 882.
Step 2: Check for other numbers that give 882 after multiplying
2 × 441 = 882
3 × 294 = 882
6 × 147 = 882
7 × 126 = 882
9 × 98 = 882
14 × 63 = 882
18 × 49 = 882
21 × 42 = 882
Therefore, the positive factor pairs of 882 are: (1, 882), (2, 441), (3, 294), (6, 147), (7, 126), (9, 98), (14, 63), (18, 49), and (21, 42).
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Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method :
Step 1: Divide 882 by 1, 882 ÷ 1 = 882.
Step 2: Continue dividing 882 by the numbers until the remainder becomes 0.
882 ÷ 1 = 882
882 ÷ 2 = 441
882 ÷ 3 = 294
882 ÷ 6 = 147
882 ÷ 7 = 126
882 ÷ 9 = 98
882 ÷ 14 = 63
882 ÷ 18 = 49
882 ÷ 21 = 42
Therefore, the factors of 882 are: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, and 882.
Prime Factors and Prime Factorization
- Multiplying prime numbers to get the given number as their product is called prime factors.
- Prime factorization is the process of breaking down the number into its prime factors.
Prime factors of 882
Divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 882 are 2, 3, and 7.
Prime Factorization of 882
Prime Factorization breaks down the prime factors of 882.
Step 1: Firstly, 882 is divided by 2 to get 441.
Step 2: Now divide 441 by 3 to get 147.
Step 3: Divide 147 by 3 to get 49.
Step 4: Divide 49 by 7 to get 7.
Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 882 is: 2 × 32 × 72.
Factor Tree of 882
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
Factor Pairs of 882
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 882:
| Factors | Positive Pair Factors |
| 1 × 882 = 882 | 1, 882 |
| 2 × 441 = 882 | 2, 441 |
| 3 × 294 = 882 | 3, 294 |
| 6 × 147 = 882 | 6, 147 |
| 7 × 126 = 882 | 7, 126 |
| 14 × 63 = 882 | 14, 63 |
| 21 × 42 = 882 | 21, 42 |
Negative factor pairs of 882:
| Factors | Negative Pair Factors |
| −1 × −882 = 882 | −1, −882 |
| −2 × −441 = 882 | −2, −441 |
| −3 × −294 = 882 | −3, −294 |
| −6 × −147 = 882 | −6, −147 |
| −7 × −126 = 882 | −7, −126 |
| −14 × −63 = 882 | −14, −63 |
| −21 × −42 = 882 | −21, −42 |
Common Mistakes and How to Avoid Them in Factors of 882
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 882, 1 and 882 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 882 consist of -1, -2, -3, 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 882/1.5 = 588, 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 882 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 882, but it has other factors like 9, 18.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 882 as 2 × 32× 72 and missing all the key factors.
Factors of 882 Examples
Problem 1
There are 9 teams and 882 participants in a competition. How will they divide them equally?
They will have 98 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
882/9 = 98
Problem 2
A field is rectangular, the length of the field is 21 meters and the total area is 882 square meters. Find the width?
42 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
882 = 21 × width
To find the value of width, we need to shift 21 to the left side.
882/21 = width
Width = 42.
Problem 3
A Walmart store in Chicago is reconciling grocery bills after fixing a state sales-tax error. The accounting system shows an 882 USD adjustment that must be divided into equal whole-dollar corrections across departments. What are all the factors of 882 that represent possible equal splits?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
Explanation
To find the factors of 882, start with its prime factorization.
882 = 2 × 3² × 7²
All factors are formed by multiplying powers of 2, 3, and 7 in every possible combination.
Each resulting number divides 882 exactly with no remainder, giving the complete factor list.
Problem 4
In a Boston middle-school science lab, students analyze pharmacy inventory data similar to systems used by CVS pharmacies. A sample contains 882 mg of a compound that must be divided into equal integer dosage units for an experiment. Which numbers are factors of 882?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
Explanation
A factor is a number that divides 882 evenly without leaving a remainder.
Using the prime factorization 2 × 3² × 7², all valid combinations of these primes produce the full set of divisors.
Each listed value allows the dosage to be split evenly.
Problem 5
An NFL team in Dallas reviews travel expenses after a road game in Houston. Based on gas prices per gallon, the team records 882 gallons of fuel usage that must be divided evenly across fuel logs. What are all the factors of 882 that allow an exact split?
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
Explanation
Equal distribution requires numbers that divide 882 with no remainder.
Because 882 has multiple divisors formed from its prime factors, there are several valid ways to split the total evenly.
All such divisors are factors of 882.
FAQs on Factors of 882
1.What are the factors of 882?
2.Mention the prime factors of 882.
3.Is 882 a multiple of 14?
4.Mention the factor pairs of 882?
5.What is the square of 882?
6.How many factors does 882 have?
7.What is the smallest factor of 882?
8.What is the largest factor of 882?
9.Which factors of 882 add up to 13?
10.How many even factors does 882 have?
11.What are the odd factors of 882?
12.What is the sum of all the factors of 882?
Important Glossaries for Factor of 882
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 882 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, and 882.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 882.
- 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 882 are (1, 882), (2, 441), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 882 is 2 × 32 × 72.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using this method for 882 gives pairs like (1, 882), (2, 441), etc.
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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.
