129 LearnersLast updated on May 26th, 2025
Factors of 2652
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 2652, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2652?
The numbers that divide 2652 evenly are known as factors of 2652.
A factor of 2652 is a number that divides the number without remainder.
The factors of 2652 are 1, 2, 3, 4, 6, 12, 13, 26, 51, 52, 102, 204, 221, 442, 663, 884, 1326, and 2652.
Negative factors of 2652: -1, -2, -3, -4, -6, -12, -13, -26, -51, -52, -102, -204, -221, -442, -663, -884, -1326, and -2652.
Prime factors of 2652: 2, 3, and 13.
Prime factorization of 2652: 2² × 3 × 13².
The sum of factors of 2652: 1 + 2 + 3 + 4 + 6 + 12 + 13 + 26 + 51 + 52 + 102 + 204 + 221 + 442 + 663 + 884 + 1326 + 2652 = 5668.
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How to Find Factors of 2652?
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 2652. Identifying the numbers which are multiplied to get the number 2652 is the multiplication method.
Step 1: Multiply 2652 by 1, 2652 × 1 = 2652.
Step 2: Check for other numbers that give 2652 after multiplying
2 × 1326 = 2652
3 × 884 = 2652
4 × 663 = 2652
6 × 442 = 2652
12 × 221 = 2652
13 × 204 = 2652
26 × 102 = 2652
51 × 52 = 2652
Therefore, the positive factor pairs of 2652 are: (1, 2652), (2, 1326), (3, 884), (4, 663), (6, 442), (12, 221), (13, 204), (26, 102), (51, 52).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 2652 by 1, 2652 ÷ 1 = 2652.
Step 2: Continue dividing 2652 by the numbers until the remainder becomes 0.
2652 ÷ 1 = 2652
2652 ÷ 2 = 1326
2652 ÷ 3 = 884
2652 ÷ 4 = 663
2652 ÷ 6 = 442
2652 ÷ 12 = 221
2652 ÷ 13 = 204
2652 ÷ 26 = 102
2652 ÷ 51 = 52
Therefore, the factors of 2652 are: 1, 2, 3, 4, 6, 12, 13, 26, 51, 52, 102, 204, 221, 442, 663, 884, 1326, 2652.
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
Prime Factorization: In this process, prime factors of 2652 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2652 ÷ 2 = 1326
1326 ÷ 2 = 663
663 ÷ 3 = 221
221 ÷ 13 = 17
17 ÷ 17 = 1
The prime factors of 2652 are 2, 3, and 13.
The prime factorization of 2652 is: 2² × 3 × 13².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2652 is divided by 2 to get 1326.
Step 2: Now divide 1326 by 2 to get 663.
Step 3: Then divide 663 by 3 to get 221.
Step 4: Divide 221 by 13 to get 17.
Here, 17 is a prime number that cannot be divided anymore.
So, the prime factorization of 2652 is: 2² × 3 × 13².
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 2652: (1, 2652), (2, 1326), (3, 884), (4, 663), (6, 442), (12, 221), (13, 204), (26, 102), (51, 52).
Negative factor pairs of 2652: (-1, -2652), (-2, -1326), (-3, -884), (-4, -663), (-6, -442), (-12, -221), (-13, -204), (-26, -102), (-51, -52).
Common Mistakes and How to Avoid Them in Factors of 2652
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 2652, 1 and 2652 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 2652 consist of -1, -2, -3, 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 2652/1.5 = 1768, 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 2652 are prime numbers.
For example, 2, 3, and 13 are the prime factors of 2652, but it has other factors like 4, 6, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 2652 as 2² × 3 × 13² and missing all the key factors.
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Factors of 2652 Examples
Problem 1
There are 6 offices and 2652 chairs. How will they divide them equally?
They will get 442 chairs each.
Explanation
To divide the chairs equally, we need to divide the total chairs by the number of offices.
2652 ÷ 6 = 442
Problem 2
A painting canvas is rectangular, with a length of 51 inches and a total area of 2652 square inches. Find the width.
52 inches.
Explanation
To find the width of the canvas, we use the formula,
Area = length × width
2652 = 51 × width
To find the value of width, we need to shift 51 to the left side.
2652 ÷ 51 = width
Width = 52
Problem 3
There are 204 boxes and 2652 candies. How many candies will be in each box?
Each box will have 13 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
2652 ÷ 204 = 13
Problem 4
In a convention, there are 2652 guests, and 12 tables. How many guests are there at each table?
There are 221 guests at each table.
Explanation
Dividing the guests by the total number of tables, we will get the number of guests at each table.
2652 ÷ 12 = 221
Problem 5
2652 apples need to be arranged in 51 baskets. How many apples will go in each basket?
Each of the baskets has 52 apples.
Explanation
Divide total apples by baskets.
2652 ÷ 51 = 52
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FAQs on Factors of 2652
1.What are the factors of 2652?
2.Mention the prime factors of 2652.
3.Is 2652 a multiple of 13?
4.Mention the factor pairs of 2652.
5.What is the square of 2652?
6.How can children in United States use numbers in everyday life to understand Factors of 2652?
7.What are some fun ways kids in United States can practice Factors of 2652 with numbers?
8.What role do numbers and Factors of 2652 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 2652 skills?
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Important Glossaries for Factor of 2652
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2652 are 1, 2, 3, 4, 6, 12, 13, 26, 51, 52, 102, 204, 221, 442, 663, 884, 1326, 2652.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 2652.
- 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 2652 are (1, 2652), (2, 1326), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 2652 is 2² × 3 × 13².
- Multiplication method: A strategy to find factor pairs by identifying numbers that multiply to give the target number. For example, using this method to find factor pairs of 2652.
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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.
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