119 LearnersLast updated on May 26th, 2025
Factors of 7056
Factors are the numbers that divide any given number evenly without 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 7056, how they are used in real life, and tips to learn them quickly.
What are the Factors of 7056?
The numbers that divide 7056 evenly are known as factors of 7056.
A factor of 7056 is a number that divides the number without remainder. The factors of 7056 include 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296, 2352, 3528, and 7056.
Negative factors of 7056: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -36, -48, -54, -72, -81, -108, -144, -162, -216, -324, -432, -648, -1296, -2352, -3528, and -7056.
Prime factors of 7056: 2 and 3.
Prime factorization of 7056: 24 × 32 × 72.
The sum of factors of 7056: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 36 + 48 + 54 + 72 + 81 + 108 + 144 + 162 + 216 + 324 + 432 + 648 + 1296 + 2352 + 3528 + 7056 = 19404
How to Find Factors of 7056?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 7056. Identifying the numbers which are multiplied to get the number 7056 is the multiplication method.
Step 1: Multiply 7056 by 1, 7056 × 1 = 7056.
Step 2: Check for other numbers that give 7056 after multiplying
2 × 3528 = 7056
3 × 2352 = 7056
4 × 1764 = 7056
6 × 1176 = 7056
8 × 882 = 7056
9 × 784 = 7056
12 × 588 = 7056
16 × 441 = 7056
18 × 392 = 7056
24 × 294 = 7056
27 × 261 = 7056
36 × 196 = 7056
48 × 147 = 7056
54 × 130.666... (not a whole number)
72 × 98 = 7056
81 × 87.111... (not a whole number)
Therefore, the positive factor pairs of 7056 are: (1, 7056), (2, 3528), (3, 2352), (4, 1764), (6, 1176), (8, 882), (9, 784), (12, 588), (16, 441), (18, 392), (24, 294), (27, 261), (36, 196), (48, 147), (72, 98).
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 7056 by 1, 7056 ÷ 1 = 7056.
Step 2: Continue dividing 7056 by the numbers until the remainder becomes 0.
7056 ÷ 1 = 7056
7056 ÷ 2 = 3528
7056 ÷ 3 = 2352
7056 ÷ 4 = 1764
7056 ÷ 6 = 1176
7056 ÷ 8 = 882
7056 ÷ 9 = 784
7056 ÷ 12 = 588
7056 ÷ 16 = 441
7056 ÷ 18 = 392
7056 ÷ 24 = 294
7056 ÷ 27 = 261
7056 ÷ 36 = 196
7056 ÷ 48 = 147
7056 ÷ 72 = 98
Therefore, the factors of 7056 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 72, 98, 147, 196, 261, 294, 392, 441, 588, 784, 882, 1176, 1764, 2352, 3528, 7056.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 7056 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
7056 ÷ 2 = 3528
3528 ÷ 2 = 1764
1764 ÷ 2 = 882
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 7056 are 2, 3, and 7.
The prime factorization of 7056 is: 24 × 32 × 72.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 7056 is divided by 2 to get 3528.
Step 2: Now divide 3528 by 2 to get 1764.
Step 3: Then divide 1764 by 2 to get 882.
Step 4: Divide 882 by 2 to get 441.
Step 5: Divide 441 by 3 to get 147.
Step 6: Divide 147 by 3 to get 49.
Step 7: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 7056 is: 24 × 32 × 72.
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 7056: (1, 7056), (2, 3528), (3, 2352), (4, 1764), (6, 1176), (8, 882), (9, 784), (12, 588), (16, 441), (18, 392), (24, 294), (27, 261), (36, 196), (48, 147), (72, 98).
Negative factor pairs of 7056: (-1, -7056), (-2, -3528), (-3, -2352), (-4, -1764), (-6, -1176), (-8, -882), (-9, -784), (-12, -588), (-16, -441), (-18, -392), (-24, -294), (-27, -261), (-36, -196), (-48, -147), (-72, -98).
Common Mistakes and How to Avoid Them in Factors of 7056
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 word. Always remember to include 1 and the number itself.
For example, in factors of 7056, 1 and 7056 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 7056 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 7056/1.5 = 4704, 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 7056 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 7056, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 7056 as 24 × 32 × 72 and missing all the key factors.
Factors of 7056 Examples
Problem 1
A group of 98 students plans a field trip, and they have $7056 to spend equally. How much will each student get?
Each student will get $72.
Explanation
To divide the money equally, we need to divide the total amount by the number of students.
7056/98 = 72
Problem 2
A community garden has a total area of 7056 square meters. If the length of one section is 108 meters, what is the width?
The width is 65.333 meters (not a whole number, recheck for proper measurements).
Explanation
To find the width of the section, we use the formula,
Area = length × width
7056 = 108 × width
To find the value of width, we need to shift 108 to the left side.
7056/108 = width
Width = 65.333
Problem 3
There are 144 crates and 7056 apples. How many apples will be in each crate?
Each crate will have 49 apples.
Explanation
To find the apples in each crate, divide the total apples by the crates.
7056/144 = 49
Problem 4
A theater has 7056 seats, and it is divided into 54 rows. How many seats are there in each row?
There are 130.666 (not a whole number) seats in each row, recheck row arrangement.
Explanation
Dividing the seats by the total rows, we will get the number of seats in each row.
7056/54 = 130.666
Problem 5
7056 bricks need to be arranged in a wall with 36 rows. How many bricks will go on each row?
Each row will have 196 bricks.
Explanation
Divide total bricks by rows.
7056/36 = 196
FAQs on Factors of 7056
1.What are the factors of 7056?
2.Mention the prime factors of 7056.
3.Is 7056 a multiple of 9?
4.Mention the factor pairs of 7056?
5.What is the square root of 7056?
6.How can children in Canada use numbers in everyday life to understand Factors of 7056?
7.What are some fun ways kids in Canada can practice Factors of 7056 with numbers?
8.What role do numbers and Factors of 7056 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 7056 skills?
Important Glossaries for Factors of 7056
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7056 include 1, 2, 3, 4, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 7056.
- 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 7056 are (1, 7056), (2, 3528), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 7056 can be expressed as 24 × 32 × 72.
- Square root: A number that, when multiplied by itself, gives the original number. For example, the square root of 7056 is approximately 84.
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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
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