123 LearnersLast updated on May 26th, 2025
Factors of 612
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 612, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 612?
The numbers that divide 612 evenly are known as factors of 612.
A factor of 612 is a number that divides the number without remainder.
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, and 612.
Negative factors of 612: -1, -2, -3, -4, -6, -9, -12, -17, -18, -34, -36, -51, -68, -102, -153, -204, -306, and -612.
Prime factors of 612: 2, 3, and 17.
Prime factorization of 612: 22 × 32 × 17. T
he sum of factors of 612: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 17 + 18 + 34 + 36 + 51 + 68 + 102 + 153 + 204 + 306 + 612 = 1638
How to Find Factors of 612?
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 612. Identifying the numbers which are multiplied to get the number 612 is the multiplication method.
Step 1: Multiply 612 by 1, 612 × 1 = 612.
Step 2: Check for other numbers that give 612 after multiplying
2 × 306 = 612
3 × 204 = 612
4 × 153 = 612
6 × 102 = 612
9 × 68 = 612
12 × 51 = 612
17 × 36 = 612
18 × 34 = 612
Therefore, the positive factor pairs of 612 are: (1, 612), (2, 306), (3, 204), (4, 153), (6, 102), (9, 68), (12, 51), (17, 36), (18, 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 612 by 1, 612 ÷ 1 = 612.
Step 2: Continue dividing 612 by the numbers until the remainder becomes 0.
612 ÷ 1 = 612
612 ÷ 2 = 306
612 ÷ 3 = 204
612 ÷ 4 = 153
612 ÷ 6 = 102
612 ÷ 9 = 68
612 ÷ 12 = 51
612 ÷ 17 = 36
612 ÷ 18 = 34
Therefore, the factors of 612 are: 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612.
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 612 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
612 ÷ 2 = 306
306 ÷ 2 = 153
153 ÷ 3 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of 612 are 2, 3, and 17.
The prime factorization of 612 is: 2^2 × 3^2 × 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, 612 is divided by 2 to get 306.
Step 2: Now divide 306 by 2 to get 153.
Step 3: Then divide 153 by 3 to get 51.
Step 4: Divide 51 by 3 to get 17. Here, 17 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 612 is: 22 × 32 × 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 612: (1, 612), (2, 306), (3, 204), (4, 153), (6, 102), (9, 68), (12, 51), (17, 36), and (18, 34).
Negative factor pairs of 612: (-1, -612), (-2, -306), (-3, -204), (-4, -153), (-6, -102), (-9, -68), (-12, -51), (-17, -36), and (-18, -34).
Common Mistakes and How to Avoid Them in Factors of 612
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 word. Always remember to include 1 and the number itself.
For example, in factors of 612, 1 and 612 is also a factor.
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 612 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 2.5 as a factor, because 612/2.5 = 244.8, 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 612 are prime numbers.
For example, 2, 3, and 17 are the prime factors of 612, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, Not breaking 612 as 2^2 × 3^2 × 17 and missing all the key factors.
Factors of 612 Examples
Problem 1
There are 12 friends and 612 marbles. How will they divide it equally?
They will get 51 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles with the number of friends.
612/12 = 51
Problem 2
A rectangular garden has a length of 34 meters and a total area of 612 square meters. Find the width.
18 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
612 = 34 × width
To find the value of width, we need to shift 34 to the left side.
612/34 = width
Width = 18.
Problem 3
There are 204 gift boxes and 612 candies. How many candies will be in each box?
Each box will have 3 candies.
Explanation
To find the candies in each box, divide the total candies with the number of boxes.
612/204 = 3
Problem 4
In a class, there are 612 students, and 17 buses. How many students are there in each bus?
There are 36 students in each bus.
Explanation
Dividing the students with the total buses, we will get the number of students in each bus.
612/17 = 36
Problem 5
612 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 68 books.
Explanation
Divide total books with shelves.
612/9 = 68
FAQs on Factors of 612
1.What are the factors of 612?
2.Mention the prime factors of 612.
3.Is 612 a multiple of 3?
4.Mention the factor pairs of 612.
5.What is the square of 612?
6.How can children in Canada use numbers in everyday life to understand Factors of 612?
7.What are some fun ways kids in Canada can practice Factors of 612 with numbers?
8.What role do numbers and Factors of 612 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 612 skills?
Important Glossaries for Factors of 612
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, and 612.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 612.
- 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 612 are (1, 612), (2, 306), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For instance, the prime factorization of 612 is 22 × 32 × 17.
- Multiple: A number that can be divided by another number without a remainder. For example, 612 is a multiple of 3.
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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.
