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 the items equally, arranging things, etc. In this topic, we will learn about the factors of 1072, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 1072 evenly are known as factors of 1072.
A factor of 1072 is a number that divides the number without remainder.
The factors of 1072 are 1, 2, 4, 8, 16, 67, 134, 268, 536, and 1072.
Negative factors of 1072: -1, -2, -4, -8, -16, -67, -134, -268, -536, and -1072.
Prime factors of 1072: 2 and 67.
Prime factorization of 1072: 2^4 × 67.
The sum of factors of 1072: 1 + 2 + 4 + 8 + 16 + 67 + 134 + 268 + 536 + 1072 = 2108
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 1072. Identifying the numbers which are multiplied to get the number 1072 is the multiplication method.
Step 1: Multiply 1072 by 1, 1072 × 1 = 1072.
Step 2: Check for other numbers that give 1072 after multiplying
2 × 536 = 1072
4 × 268 = 1072
8 × 134 = 1072
16 × 67 = 1072
Therefore, the positive factor pairs of 1072 are: (1, 1072), (2, 536), (4, 268), (8, 134), (16, 67).
All these factor pairs result in 1072.
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 1072 by 1, 1072 ÷ 1 = 1072.
Step 2: Continue dividing 1072 by the numbers until the remainder becomes 0.
1072 ÷ 1 = 1072
1072 ÷ 2 = 536
1072 ÷ 4 = 268
1072 ÷ 8 = 134
1072 ÷ 16 = 67
Therefore, the factors of 1072 are: 1, 2, 4, 8, 16, 67, 134, 268, 536, 1072.
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 1072 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1072 ÷ 2 = 536
536 ÷ 2 = 268
268 ÷ 2 = 134
134 ÷ 2 = 67
67 ÷ 67 = 1
The prime factors of 1072 are 2 and 67.
The prime factorization of 1072 is: 2^4 × 67.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1072 is divided by 2 to get 536.
Step 2: Now divide 536 by 2 to get 268
Step 3: Then divide 268 by 2 to get 134.
Step 4: Divide 134 by 2 to get 67.
Here, 67 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1072 is: 2^4 × 67.
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 1072: (1, 1072), (2, 536), (4, 268), (8, 134), and (16, 67).
Negative factor pairs of 1072: (-1, -1072), (-2, -536), (-4, -268), (-8, -134), and (-16, -67).
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 8 friends and 1072 candies. How will they divide it equally?
They will get 134 candies each.
To divide the candies equally, we need to divide the total candies by the number of friends.
1072/8 = 134
A rectangular garden has a width of 16 meters and a total area of 1072 square meters. Find the length.
67 meters.
To find the length of the garden, we use the formula,
Area = length × width
1072 = length × 16
To find the value of the length, we need to shift 16 to the left side.
1072/16 = length
Length = 67.
There are 67 baskets and 1072 apples. How many apples will be in each basket?
Each basket will have 16 apples.
To find the apples in each basket, divide the total apples by the baskets.
1072/67 = 16
A company has 1072 employees, and they want to form 16 teams. How many employees will be in each team?
There are 67 employees in each team.
Dividing the employees by the total teams, we will get the number of employees in each team.
1072/16 = 67
1072 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has 268 books.
Divide total books by shelves.
1072/4 = 268
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.