101 LearnersLast updated on May 26th, 2025
Factors of 7575
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 7575, how they are used in real life, and tips to learn them quickly.
What are the Factors of 7575?
The numbers that divide 7575 evenly are known as factors of 7575.
A factor of 7575 is a number that divides the number without remainder.
The factors of 7575 are 1, 3, 5, 15, 505, 1515, 2525, and 7575.
Negative factors of 7575: -1, -3, -5, -15, -505, -1515, -2525, and -7575.
Prime factors of 7575: 3, 5, 101.
Prime factorization of 7575: 3 × 5 × 505.
The sum of factors of 7575: 1 + 3 + 5 + 15 + 505 + 1515 + 2525 + 7575 = 12144
How to Find Factors of 7575?
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 7575. Identifying the numbers which are multiplied to get the number 7575 is the multiplication method.
Step 1: Multiply 7575 by 1, 7575 × 1 = 7575.
Step 2: Check for other numbers that give 7575 after multiplying
3 × 2525 = 7575
5 × 1515 = 7575
15 × 505 = 7575
Therefore, the positive factor pairs of 7575 are: (1, 7575), (3, 2525), (5, 1515), (15, 505).
All these factor pairs result in 7575.
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 in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 7575 by 1, 7575 ÷ 1 = 7575.
Step 2: Continue dividing 7575 by the numbers until the remainder becomes 0.
7575 ÷ 1 = 7575
7575 ÷ 3 = 2525
7575 ÷ 5 = 1515
7575 ÷ 15 = 505
Therefore, the factors of 7575 are: 1, 3, 5, 15, 505, 1515, 2525, 7575.
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 7575 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
7575 ÷ 3 = 2525
2525 ÷ 5 = 505
505 ÷ 5 = 101
101 ÷ 101 = 1
The prime factors of 7575 are 3, 5, and 101.
The prime factorization of 7575 is: 3 × 5 × 101.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 7575 is divided by 3 to get 2525.
Step 2: Now divide 2525 by 5 to get 505.
Step 3: Then divide 505 by 5 to get 101.
Step 4: 101 is a prime number and cannot be divided further.
So, the prime factorization of 7575 is: 3 × 5 × 101.
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 7575: (1, 7575), (3, 2525), (5, 1515), (15, 505).
Negative factor pairs of 7575: (-1, -7575), (-3, -2525), (-5, -1515), (-15, -505).
Common Mistakes and How to Avoid Them in Factors of 7575
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 7575, 1 and 7575 is also a factor.
Factors of 7575 Examples
Problem 1
A cultural event has 7575 tickets, and each person can buy up to 5 tickets. How many people can buy the maximum number of tickets?
1515 people can buy the maximum number of tickets.
Explanation
To find the number of people who can buy the maximum number of tickets, divide the total tickets by the number of tickets a person can buy.
7575 ÷ 5 = 1515
Problem 2
There are 3 concerts, and each concert has an equal number of seats totaling 7575. How many seats are there per concert?
2525 seats per concert.
Explanation
To find the number of seats per concert, we use the formula:
Total seats = number of concerts × seats per concert
7575 = 3 × seats per concert
To find the value of seats per concert, shift 3 to the left side.
7575 ÷ 3 = seats per concert
Seats per concert = 2525.
Problem 3
A shop has 505 boxes of items, each containing the same number of items, totaling 7575 items. How many items are in each box?
Each box contains 15 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
7575 ÷ 505 = 15
Problem 4
A community event has 7575 participants, and each group has 3 leaders. How many groups are there in the event?
There are 2525 groups in the event.
Explanation
Dividing the participants by the number of leaders gives the number of groups.
7575 ÷ 3 = 2525
Problem 5
7575 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each shelf will have 505 books.
Explanation
Divide total books by shelves.
7575 ÷ 15 = 505
FAQs on Factors of 7575
1.What are the factors of 7575?
2.Mention the prime factors of 7575.
3.Is 7575 a multiple of 5?
4.Mention the factor pairs of 7575.
5.What is the square of 7575?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 7575?
7.What are some fun ways kids in Indonesia can practice Factors of 7575 with numbers?
8.What role do numbers and Factors of 7575 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 7575 skills?
Important Glossaries for Factors of 7575
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7575 are 1, 3, 5, 15, 505, 1515, 2525, and 7575.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 101 are prime factors of 7575.
- 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 7575 are (1, 7575), (3, 2525), etc.
- Prime factorization: Breaking down a number into its prime factors. For instance, 7575 can be factorized into 3 × 5 × 101.
- Multiplication method: A method to find factors by identifying pairs of numbers multiplied to give a specific number, such as 7575.
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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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