Last updated on May 28th, 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 1312, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 1312 evenly are known as factors of 1312.
A factor of 1312 is a number that divides the number without a remainder.
The factors of 1312 are 1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, and 1312.
Negative factors of 1312: -1, -2, -4, -8, -16, -32, -41, -82, -164, -328, -656, and -1312.
Prime factors of 1312: 2 and 41.
Prime factorization of 1312: 25 × 41.
The sum of factors of 1312: 1 + 2 + 4 + 8 + 16 + 32 + 41 + 82 + 164 + 328 + 656 + 1312 = 2646
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 1312. Identifying the numbers which are multiplied to get the number 1312 is the multiplication method.
Step 1: Multiply 1312 by 1, 1312 × 1 = 1312.
Step 2: Check for other numbers that give 1312 after multiplying
2 × 656 = 1312
4 × 328 = 1312
8 × 164 = 1312
16 × 82 = 1312
32 × 41 = 1312
Therefore, the positive factor pairs of 1312 are: (1, 1312), (2, 656), (4, 328), (8, 164), (16, 82), (32, 41).
For every positive factor, there is a negative factor.
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1312 by 1, 1312 ÷ 1 = 1312.
Step 2: Continue dividing 1312 by the numbers until the remainder becomes 0.
1312 ÷ 1 = 1312
1312 ÷ 2 = 656
1312 ÷ 4 = 328
1312 ÷ 8 = 164
1312 ÷ 16 = 82
1312 ÷ 32 = 41
Therefore, the factors of 1312 are: 1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, 1312.
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 1312 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1312 ÷ 2 = 656
656 ÷ 2 = 328
328 ÷ 2 = 164
164 ÷ 2 = 82
82 ÷ 2 = 41
41 ÷ 41 = 1
The prime factors of 1312 are 2 and 41.
The prime factorization of 1312 is: 25 × 41.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1312 is divided by 2 to get 656.
Step 2: Now divide 656 by 2 to get 328.
Step 3: Then divide 328 by 2 to get 164.
Step 4: Divide 164 by 2 to get 82.
Step 5: Divide 82 by 2 to get 41.
Here, 41 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1312 is: 25 × 41.
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 1312: (1, 1312), (2, 656), (4, 328), (8, 164), (16, 82), (32, 41).
Negative factor pairs of 1312: (-1, -1312), (-2, -656), (-4, -328), (-8, -164), (-16, -82), (-32, -41).
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 16 students and 1312 pages of a book. How many pages will each student get if divided equally?
Each student will get 82 pages.
To divide the pages equally, we need to divide the total pages by the number of students.
1312/16 = 82
A hall is rectangular, the length of the hall is 41 meters and the total area is 1312 square meters. Find the width.
32 meters.
To find the width of the hall, we use the formula,
Area = length × width
1312 = 41 × width
To find the value of width, we need to shift 41 to the left side.
1312/41 = width
Width = 32.
There are 164 boxes and 1312 candies. How many candies will be in each box?
Each box will have 8 candies.
To find the candies in each box, divide the total candies by the boxes.
1312/164 = 8
In a workshop, there are 82 machines and a total of 1312 tasks. How many tasks are assigned to each machine?
There are 16 tasks assigned to each machine.
Dividing the tasks by the total machines, we will get the number of tasks for each machine.
1312/82 = 16
1312 chairs need to be arranged in 41 rows. How many chairs will go in each row?
Each of the rows has 32 chairs.
Divide the total chairs by the rows.
1312/41 = 32
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.