100 LearnersLast updated on May 26th, 2025
Factors of 1275
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 1275, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1275?
The numbers that divide 1275 evenly are known as factors of 1275.
A factor of 1275 is a number that divides the number without remainder.
The factors of 1275 are 1, 3, 5, 15, 17, 25, 51, 85, 255, 425, and 1275.
Negative factors of 1275: -1, -3, -5, -15, -17, -25, -51, -85, -255, -425, and -1275.
Prime factors of 1275: 3, 5, and 17.
Prime factorization of 1275: 3 × 52 × 17.
The sum of factors of 1275: 1 + 3 + 5 + 15 + 17 + 25 + 51 + 85 + 255 + 425 + 1275 = 2157
How to Find Factors of 1275?
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 1275. Identifying the numbers that are multiplied to get the number 1275 is the multiplication method.
Step 1: Multiply 1275 by 1, 1275 × 1 = 1275.
Step 2: Check for other numbers that give 1275 after multiplying:
3 × 425 = 1275
5 × 255 = 1275
15 × 85 = 1275
17 × 75 = 1275
25 × 51 = 1275
Therefore, the positive factor pairs of 1275 are: (1, 1275), (3, 425), (5, 255), (15, 85), (17, 75), (25, 51).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number by whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated using a simple division method:
Step 1: Divide 1275 by 1, 1275 ÷ 1 = 1275.
Step 2: Continue dividing 1275 by the numbers until the remainder becomes 0.
1275 ÷ 1 = 1275
1275 ÷ 3 = 425
1275 ÷ 5 = 255
1275 ÷ 15 = 85
1275 ÷ 17 = 75
1275 ÷ 25 = 51
Therefore, the factors of 1275 are: 1, 3, 5, 15, 17, 25, 51, 85, 255, 425, 1275.
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 1275 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1275 ÷ 3 = 425
425 ÷ 5 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 1275 are 3, 5, and 17.
The prime factorization of 1275 is: 3 × 5^2 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1275 is divided by 3 to get 425.
Step 2: Now divide 425 by 5 to get 85.
Step 3: Then divide 85 by 5 to get 17.
Here, 17 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1275 is: 3 × 52 × 17.
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 1275: (1, 1275), (3, 425), (5, 255), (15, 85), (17, 75), (25, 51).
Negative factor pairs of 1275: (-1, -1275), (-3, -425), (-5, -255), (-15, -85), (-17, -75), (-25, -51).
Common Mistakes and How to Avoid Them in Factors of 1275
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1275, 1 and 1275 are also factors.
Factors of 1275 Examples
Problem 1
There are 3 tables and 1275 marbles. How will they distribute them equally?
They will distribute 425 marbles on each table.
Explanation
To distribute the marbles equally, divide the total marbles by the number of tables.
1275/3 = 425
Problem 2
A garden is rectangular, the length of the garden is 25 meters and the total area is 1275 square meters. Find the width?
51 meters.
Explanation
To find the width of the garden, use the formula,
Area = length × width
1275 = 25 × width
To find the value of width, shift 25 to the left side.
1275/25 = width
Width = 51.
Problem 3
There are 17 baskets and 1275 apples. How many apples will be in each basket?
Each basket will have 75 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
1275/17 = 75
Problem 4
In a school, there are 1275 students, and 5 classes. How many students are there in each class?
There are 255 students in each class.
Explanation
Dividing the students by the total classes, we get the number of students in each class.
1275/5 = 255
Problem 5
1275 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each shelf will have 85 books.
Explanation
Divide the total books by the number of shelves.
1275/15 = 85
FAQs on Factors of 1275
1.What are the factors of 1275?
2.Mention the prime factors of 1275.
3.Is 1275 a multiple of 5?
4.Mention the factor pairs of 1275?
5.What is the square of 1275?
Important Glossaries for Factors of 1275
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1275 are 1, 3, 5, 15, 17, 25, 51, 85, 255, 425, 1275.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 17 are prime factors of 1275.
- 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 1275 are (1, 1275), (3, 425), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1275 is 3 × 5^2 × 17.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method for 1275 involves finding pairs like (3, 425).
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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.
