Last updated on May 26th, 2025
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 812, how they are used in real life, and tips to learn them quickly.
The numbers that divide 812 evenly are known as factors of 812.
A factor of 812 is a number that divides the number without a remainder.
The factors of 812 are 1, 2, 4, 7, 14, 29, 58, 116, 203, 406, and 812.
Negative factors of 812: -1, -2, -4, -7, -14, -29, -58, -116, -203, -406, and -812.
Prime factors of 812: 2, 7, and 29.
Prime factorization of 812: 2² × 7 × 29.
The sum of factors of 812: 1 + 2 + 4 + 7 + 14 + 29 + 58 + 116 + 203 + 406 + 812 = 1652
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 812. Identifying the numbers which are multiplied to get the number 812 is the multiplication method.
Step 1: Multiply 812 by 1, 812 × 1 = 812.
Step 2: Check for other numbers that give 812 after multiplying
2 × 406 = 812
4 × 203 = 812
7 × 116 = 812
14 × 58 = 812
29 × 28 = 812
Therefore, the positive factor pairs of 812 are: (1, 812), (2, 406), (4, 203), (7, 116), (14, 58), and (29, 28).
For every positive factor, there is a negative factor.
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 812 by 1, 812 ÷ 1 = 812.
Step 2: Continue dividing 812 by the numbers until the remainder becomes 0.
812 ÷ 1 = 812
812 ÷ 2 = 406
812 ÷ 4 = 203
812 ÷ 7 = 116
812 ÷ 14 = 58
812 ÷ 29 = 28
Therefore, the factors of 812 are: 1, 2, 4, 7, 14, 29, 58, 116, 203, 406, and 812.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 812 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
812 ÷ 2 = 406
406 ÷ 2 = 203
203 ÷ 7 = 29
29 ÷ 29 = 1
The prime factors of 812 are 2, 7, and 29.
The prime factorization of 812 is: 2² × 7 × 29.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 812 is divided by 2 to get 406.
Step 2: Now divide 406 by 2 to get 203.
Step 3: Then divide 203 by 7 to get 29. Here, 29 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 812 is: 2² × 7 × 29.
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 812: (1, 812), (2, 406), (4, 203), (7, 116), (14, 58), and (29, 28).
Negative factor pairs of 812: (-1, -812), (-2, -406), (-4, -203), (-7, -116), (-14, -58), and (-29, -28).
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 812 candies to be packed into boxes with each box holding 29 candies. How many full boxes can be packed?
28 full boxes can be packed.
To find the number of full boxes, divide the total candies by the number of candies each box holds.
812/29 = 28
A rectangular plot has a length of 58 meters and a total area of 812 square meters. Find the width.
14 meters.
To find the width of the plot, we use the formula, Area = length × width
812 = 58 × width
To find the value of width, divide the area by the length.
812/58 = width
Width = 14.
There are 116 oranges and 812 boxes. How many boxes will have oranges if each box can hold only one orange?
116 boxes will have oranges.
To find out how many boxes will have oranges, divide the total number of oranges by the capacity of each box.
812/116 = 7
A class of 406 students needs to be divided into 29 groups. How many students will be in each group?
14 students will be in each group.
Dividing the students by the total groups gives the number of students in each group.
406/29 = 14
A warehouse has 58 shelves and 812 items. How many items will be on each shelf if distributed equally?
Each shelf will have 14 items.
Divide the total items by the number of shelves.
812/58 = 14
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.