121 LearnersLast updated on May 26th, 2025
Factors of 1072
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.
What are the Factors of 1072?
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
How to Find Factors of 1072?
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 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.
Finding Factors Using Division Method
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.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of 1072
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 number. Always remember to include 1 and the number itself.
For example, in factors of 1072, 1 and 1072 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 1072 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1072/1.5 = 714.666..., 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 1072 are prime numbers.
For example, 2 and 67 are the prime factors of 1072, but it has other factors like 4, 134.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1072 as 2^4 × 67 and missing all the key factors.
Factors of 1072 Examples
Problem 1
There are 8 friends and 1072 candies. How will they divide it equally?
They will get 134 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
1072/8 = 134
Problem 2
A rectangular garden has a width of 16 meters and a total area of 1072 square meters. Find the length.
67 meters.
Explanation
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.
Problem 3
There are 67 baskets and 1072 apples. How many apples will be in each basket?
Each basket will have 16 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1072/67 = 16
Problem 4
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.
Explanation
Dividing the employees by the total teams, we will get the number of employees in each team.
1072/16 = 67
Problem 5
1072 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has 268 books.
Explanation
Divide total books by shelves.
1072/4 = 268
FAQs on Factors of 1072
1.What are the factors of 1072?
2.Mention the prime factors of 1072.
3.Is 1072 a multiple of 4?
4.Mention the factor pairs of 1072?
5.What is the square of 1072?
Important Glossaries for Factor of 1072
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1072 are 1, 2, 4, 8, 16, 67, 134, 268, 536, and 1072.
- Prime factors: The factors which are prime numbers. For example, 2 and 67 are prime factors of 1072.
- 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 1072 are (1, 1072), (2, 536), (4, 268), etc.
- Prime factorization: The expression of a number as the product of prime numbers. For 1072, it is 2^4 × 67.
- Multiple: A number that can be divided by another number without a remainder. For example, 1072 is a multiple of 4.
Explore More numbers
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.
