102 LearnersLast updated on May 26th, 2025
Factors of 850
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 850, how they are used in real life, and tips to learn them quickly.
What are the Factors of 850?
The numbers that divide 850 evenly are known as factors of 850.
A factor of 850 is a number that divides the number without a remainder.
The factors of 850 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, and 850.
Negative factors of 850: -1, -2, -5, -10, -17, -25, -34, -50, -85, -170, -425, and -850.
Prime factors of 850: 2, 5, and 17.
Prime factorization of 850: 2 × 52 × 17.
The sum of factors of 850: 1 + 2 + 5 + 10 + 17 + 25 + 34 + 50 + 85 + 170 + 425 + 850 = 1674
How to Find Factors of 850?
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 850. Identifying the numbers which are multiplied to get the number 850 is the multiplication method.
Step 1: Multiply 850 by 1, 850 × 1 = 850.
Step 2: Check for other numbers that give 850 after multiplying:
2 × 425 = 850
5 × 170 = 850
10 × 85 = 850
17 × 50 = 850
25 × 34 = 850
Therefore, the positive factor pairs of 850 are: (1, 850), (2, 425), (5, 170), (10, 85), (17, 50), and (25, 34).
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 850 by 1, 850 ÷ 1 = 850.
Step 2: Continue dividing 850 by the numbers until the remainder becomes 0.
850 ÷ 1 = 850
850 ÷ 2 = 425
850 ÷ 5 = 170
850 ÷ 10 = 85
850 ÷ 17 = 50
850 ÷ 25 = 34
Therefore, the factors of 850 are: 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 850 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
850 ÷ 2 = 425
425 ÷ 5 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 850 are 2, 5, and 17.
The prime factorization of 850 is: 2 × 5^2 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 850 is divided by 2 to get 425.
Step 2: Now divide 425 by 5 to get 85.
Step 3: Then divide 85 by 5 to get 17.
Step 4: Here, 17 is a prime number and cannot be divided further. So, the prime factorization of 850 is: 2 × 52 × 17.
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 850: (1, 850), (2, 425), (5, 170), (10, 85), (17, 50), and (25, 34).
Negative factor pairs of 850: (-1, -850), (-2, -425), (-5, -170), (-10, -85), (-17, -50), and (-25, -34).
Common Mistakes and How to Avoid Them in Factors of 850
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 850, 1 and 850 are also factors.
Factors of 850 Examples
Problem 1
There are 17 friends and 850 candies. How will they divide them equally?
They will get 50 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
850/17 = 50
Problem 2
A field is rectangular, the length of the field is 25 meters and the total area is 850 square meters. Find the width?
34 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
850 = 25 × width
To find the value of width, we need to shift 25 to the left side.
850/25 = width
Width = 34.
Problem 3
There are 50 bags and 850 apples. How many apples will be in each bag?
Each bag will have 17 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
850/50 = 17
Problem 4
In a class, there are 850 students, and 10 groups. How many students are there in each group?
There are 85 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
850/10 = 85
Problem 5
850 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 170 books.
Explanation
Divide total books by shelves.
850/5 = 170
FAQs on Factors of 850
1.What are the factors of 850?
2.Mention the prime factors of 850.
3.Is 850 a multiple of 5?
4.Mention the factor pairs of 850?
5.What is the square of 850?
Important Glossaries for Factors of 850
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 850 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, and 850.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 17 are prime factors of 850.
- 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 850 are (1, 850), (2, 425), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 850 is 2 × 52 × 17.
- Multiple: A number that can be divided by another number without a remainder. For instance, 850 is a multiple of 5.
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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.
