119 LearnersLast updated on May 26th, 2025
Factors of 1325
Factors are the numbers that divide any given number evenly without a 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 1325, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1325?
The numbers that divide 1325 evenly are known as factors of 1325.
A factor of 1325 is a number that divides the number without a remainder.
The factors of 1325 are 1, 5, 13, 25, 53, 65, 265, and 1325.
Negative factors of 1325: -1, -5, -13, -25, -53, -65, -265, and -1325.
Prime factors of 1325: 5 and 53.
Prime factorization of 1325: 5 × 53.
The sum of factors of 1325: 1 + 5 + 13 + 25 + 53 + 65 + 265 + 1325 = 1752
How to Find Factors of 1325?
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 1325. Identifying the numbers that are multiplied to get the number 1325 is the multiplication method.
Step 1: Multiply 1325 by 1, 1325 × 1 = 1325.
Step 2: Check for other numbers that give 1325 after multiplying:
5 × 265 = 1325
13 × 102 = 1325
25 × 53 = 1325
Therefore, the positive factor pairs of 1325 are: (1, 1325), (5, 265), (13, 102), (25, 53).
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 a whole number as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1325 by 1, 1325 ÷ 1 = 1325.
Step 2: Continue dividing 1325 by the numbers until the remainder becomes 0.
1325 ÷ 1 = 1325
1325 ÷ 5 = 265
1325 ÷ 13 = 102
1325 ÷ 25 = 53
Therefore, the factors of 1325 are: 1, 5, 13, 25, 53, 65, 265, 1325.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1325 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1325 ÷ 5 = 265
265 ÷ 5 = 53
53 ÷ 53 = 1
The prime factors of 1325 are 5 and 53.
The prime factorization of 1325 is: 5 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1325 is divided by 5 to get 265.
Step 2: Now divide 265 by 5 to get 53.
Step 3: Here, 53 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1325 is: 5 × 53.
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 1325: (1, 1325), (5, 265), (13, 102), (25, 53).
Negative factor pairs of 1325: (-1, -1325), (-5, -265), (-13, -102), (-25, -53).
Common Mistakes and How to Avoid Them in Factors of 1325
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 1325, 1 and 1325 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 1325 consist of -1, -5, -13, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 2.5 as a factor, because 1325/2.5 = 530, 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 1325 are prime numbers.
For example, 5 and 53 are the prime factors of 1325, but it has other factors like 25, 65.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1325 as 5 × 53 and missing all the key factors.
Factors of 1325 Examples
Problem 1
There are 5 teams and 1325 apples. How will they divide it equally?
They will get 265 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of teams.
1325/5 = 265
Problem 2
A rectangular garden has a length of 25 meters and a total area of 1325 square meters. Find the width.
53 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1325 = 25 × width
To find the value of width, we need to shift 25 to the left side.
1325/25 = width
Width = 53.
Problem 3
There are 13 boxes and 1325 marbles. How many marbles will be in each box?
Each box will have 102 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
1325/13 = 102
Problem 4
In a class, there are 1325 students, and 5 groups. How many students are there in each group?
There are 265 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1325/5 = 265
Problem 5
1325 books need to be arranged in 53 shelves. How many books will go on each shelf?
Each of the shelves has 25 books.
Explanation
Divide total books with shelves.
1325/53 = 25
FAQs on Factors of 1325
1.What are the factors of 1325?
2.Mention the prime factors of 1325.
3.Is 1325 a multiple of 25?
4.Mention the factor pairs of 1325?
5.What is the square of 1325?
Important Glossaries for Factors of 1325
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1325 are 1, 5, 13, 25, 53, 65, 265, and 1325.
- Prime factors: The factors which are prime numbers. For example, 5 and 53 are prime factors of 1325.
- 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 1325 are (1, 1325), (5, 265), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1325 is 5 × 53.
- Negative factors: Factors that are negative integers. For example, -1, -5, -13, -25, etc., are negative factors of 1325.
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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.
