Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 12 friends and 612 marbles. How will they divide it equally?
They will get 51 marbles each.
To divide the marbles equally, we need to divide the total marbles with the number of friends.
612/12 = 51
A rectangular garden has a length of 34 meters and a total area of 612 square meters. Find the width.
18 meters.
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.
There are 204 gift boxes and 612 candies. How many candies will be in each box?
Each box will have 3 candies.
To find the candies in each box, divide the total candies with the number of boxes.
612/204 = 3
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.
Dividing the students with the total buses, we will get the number of students in each bus.
612/17 = 36
612 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 68 books.
Divide total books with shelves.
612/9 = 68
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.
: She loves to read number jokes and games.