132 LearnersLast updated on May 26th, 2025
Factors of 1056
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 1056, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1056?
The numbers that divide 1056 evenly are known as factors of 1056.
A factor of 1056 is a number that divides the number without remainder.
The factors of 1056 are 1, 2, 3, 4, 6, 8, 12, 16, 22, 24, 32, 44, 48, 66, 88, 132, 176, 264, 352, 528, and 1056.
Negative factors of 1056: -1, -2, -3, -4, -6, -8, -12, -16, -22, -24, -32, -44, -48, -66, -88, -132, -176, -264, -352, -528, and -1056.
Prime factors of 1056: 2 and 3.
Prime factorization of 1056: 25 × 3 × 11.
The sum of factors of 1056: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 22 + 24 + 32 + 44 + 48 + 66 + 88 + 132 + 176 + 264 + 352 + 528 + 1056 = 3456
How to Find Factors of 1056?
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 1056. Identifying the numbers which are multiplied to get the number 1056 is the multiplication method.
Step 1: Multiply 1056 by 1, 1056 × 1 = 1056.
Step 2: Check for other numbers that give 1056 after multiplying
2 × 528 = 1056
3 × 352 = 1056
4 × 264 = 1056
6 × 176 = 1056
8 × 132 = 1056
11 × 96 = 1056
16 × 66 = 1056
22 × 48 = 1056
24 × 44 = 1056
32 × 33 = 1056
Therefore, the positive factor pairs of 1056 are: (1, 1056), (2, 528), (3, 352), (4, 264), (6, 176), (8, 132), (11, 96), (16, 66), (22, 48), (24, 44), and (32, 33). 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 1056 by 1, 1056 ÷ 1 = 1056.
Step 2: Continue dividing 1056 by the numbers until the remainder becomes 0.
1056 ÷ 1 = 1056
1056 ÷ 2 = 528
1056 ÷ 3 = 352
1056 ÷ 4 = 264
1056 ÷ 6 = 176
1056 ÷ 8 = 132
1056 ÷ 11 = 96
1056 ÷ 16 = 66
1056 ÷ 22 = 48
1056 ÷ 24 = 44
1056 ÷ 32 = 33
Therefore, the factors of 1056 are: 1, 2, 3, 4, 6, 8, 11, 16, 22, 24, 32, 33, 44, 48, 66, 88, 132, 176, 264, 352, 528, and 1056.
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 1056 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1056 ÷ 2 = 528
528 ÷ 2 = 264
264 ÷ 2 = 132
132 ÷ 2 = 66
66 ÷ 2 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 1056 are 2, 3, and 11.
The prime factorization of 1056 is: 25 × 3 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1056 is divided by 2 to get 528.
Step 2: Now divide 528 by 2 to get 264.
Step 3: Then divide 264 by 2 to get 132.
Step 4: Divide 132 by 2 to get 66.
Step 5: Divide 66 by 2 to get 33.
Step 6: Divide 33 by 3 to get 11.
Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1056 is: 25 × 3 × 11.
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 1056: (1, 1056), (2, 528), (3, 352), (4, 264), (6, 176), (8, 132), (11, 96), (16, 66), (22, 48), (24, 44), and (32, 33).
Negative factor pairs of 1056: (-1, -1056), (-2, -528), (-3, -352), (-4, -264), (-6, -176), (-8, -132), (-11, -96), (-16, -66), (-22, -48), (-24, -44), and (-32, -33).
Common Mistakes and How to Avoid Them in Factors of 1056
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 1056, 1 and 1056 are also factors.
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 1056 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1056/1.5 = 704, 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 1056 are prime numbers.
For example, 2, 3, and 11 are the prime factors of 1056, but it has other factors like 4, 6, 8, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1056 as 2^5 × 3 × 11 and missing all the key factors.
Factors of 1056 Examples
Problem 1
There are 22 friends and 1056 candies. How will they divide it equally?
They will get 48 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
1056/22 = 48
Problem 2
A field is rectangular, the length of the field is 32 meters and the total area is 1056 square meters. Find the width?
33 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
1056 = 32 × width
To find the value of width, we need to shift 32 to the left side.
1056/32 = width
Width = 33.
Problem 3
There are 66 bags and 1056 candies. How many candies will be in each bag?
Each bag will have 16 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
1056/66 = 16
Problem 4
In a class, there are 1056 students, and 88 groups. How many students are there in each group?
There are 12 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1056/88 = 12
Problem 5
1056 books need to be arranged in 44 shelves. How many books will go on each shelf?
Each of the shelves has 24 books.
Explanation
Divide total books with shelves. 1056/44 = 24
FAQs on Factors of 1056
1.What are the factors of 1056?
2.Mention the prime factors of 1056.
3.Is 1056 a multiple of 12?
4.Mention the factor pairs of 1056?
5.What is the square of 1056?
Important Glossaries for Factor of 1056
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1056 are 1, 2, 3, 4, 6, 8, 11, 16, 22, 24, 32, 33, 44, 48, 66, 88, 132, 176, 264, 352, 528, and 1056.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 1056.
- 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 1056 are (1, 1056), (2, 528), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1056 is 2^5 × 3 × 11.
- Negative factors: Factors that are negative numbers. For example, the negative factors of 1056 are -1, -2, -3, -4, -6, -8, etc.
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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.
