112 LearnersLast updated on May 26th, 2025
Factors of 636
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 636, how they are used in real life, and tips to learn them quickly.
What are the Factors of 636?
The numbers that divide 636 evenly are known as factors of 636. A factor of 636 is a number that divides the number without a remainder. The factors of 636 are 1, 2, 3, 4, 6, 9, 12, 18, 53, 106, 159, 212, 318, and 636.
Negative factors of 636: -1, -2, -3, -4, -6, -9, -12, -18, -53, -106, -159, -212, -318, and -636.
Prime factors of 636: 2, 3, and 53.
Prime factorization of 636: 2² × 3 × 53.
The sum of factors of 636: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 53 + 106 + 159 + 212 + 318 + 636 = 1539
How to Find Factors of 636?
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 636. Identifying the numbers which are multiplied to get the number 636 is the multiplication method.
Step 1: Multiply 636 by 1, 636 × 1 = 636.
Step 2: Check for other numbers that give 636 after multiplying
2 × 318 = 636
3 × 212 = 636
4 × 159 = 636
6 × 106 = 636
9 × 53 = 636
Therefore, the positive factor pairs of 636 are: (1, 636), (2, 318), (3, 212), (4, 159), (6, 106), and (9, 53). All these factor pairs result in 636. 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 636 by 1, 636 ÷ 1 = 636.
Step 2: Continue dividing 636 by the numbers until the remainder becomes 0.
636 ÷ 1 = 636
636 ÷ 2 = 318
636 ÷ 3 = 212
636 ÷ 4 = 159
636 ÷ 6 = 106
636 ÷ 9 = 53
Therefore, the factors of 636 are: 1, 2, 3, 4, 6, 9, 12, 18, 53, 106, 159, 212, 318, and 636.
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 636 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
636 ÷ 2 = 318
318 ÷ 2 = 159
159 ÷ 3 = 53
53 ÷ 53 = 1
The prime factors of 636 are 2, 3, and 53.
The prime factorization of 636 is: 2² × 3 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 636 is divided by 2 to get 318.
Step 2: Now divide 318 by 2 to get 159.
Step 3: Then divide 159 by 3 to get 53. Here, 53 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 636 is: 2² × 3 × 53.
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 636: (1, 636), (2, 318), (3, 212), (4, 159), (6, 106), and (9, 53).
- Negative factor pairs of 636: (-1, -636), (-2, -318), (-3, -212), (-4, -159), (-6, -106), and (-9, -53).
Common Mistakes and How to Avoid Them in Factors of 636
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 636, 1 and 636 are also factors.
Factors of 636 Examples
Problem 1
A charity wants to distribute 636 meals equally among 53 families. How many meals will each family receive?
Each family will receive 12 meals.
Explanation
To divide the meals equally, we need to divide the total meals by the number of families. 636/53 = 12
Problem 2
A rectangular garden has a length of 18 meters and a total area of 636 square meters. Find the width of the garden.
The width is 35.33 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
636 = 18 × width
To find the value of width, we need to shift 18 to the left side.
636/18 = width
Width ≈ 35.33.
Problem 3
If a company wants to pack 636 items equally into 106 boxes, how many items will each box contain?
Each box will contain 6 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
636/106 = 6
Problem 4
There are 636 students, and they need to be divided into 12 groups. How many students will there be in each group?
There will be 53 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
636/12 = 53
Problem 5
A teacher has 636 books and wants to arrange them in 9 shelves. How many books will go on each shelf?
Each of the shelves will have 70.67 books.
Explanation
Divide total books by the shelves.
636/9 ≈ 70.67
FAQs on Factors of 636
1.What are the factors of 636?
2.Mention the prime factors of 636.
3.Is 636 a multiple of 4?
4.Mention the factor pairs of 636?
5.What is the square of 636?
Important Glossaries for Factors of 636
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 636 are 1, 2, 3, 4, 6, 9, 12, 18, 53, 106, 159, 212, 318, and 636.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 53 are prime factors of 636.
- 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 636 are (1, 636), (2, 318), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 636 is 2² × 3 × 53.
- Multiplication method: A method for finding factors by identifying the pairs of numbers that multiply to give the target number. For example, the multiplication method for 636 includes pairs like (2, 318) and (3, 212).
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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.
