287 LearnersLast updated on May 26th, 2025
Factors of 525
Factors of 525 are numbers that can divide 525 completely without any remainder. We often use factors like organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 525 and the different methods to find them.
What are the Factors of 525?
The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, and 525.
Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -3, -5, -7, -15, -21, -25, -35, -75, -105, -175, -525
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 525 as the product.
Prime factors: 3, 5, 7
Prime Factorization:
The simplification of the number 525 using the prime factors of 525.
It is expressed as 31 × 52 × 71
Table of Factors of 525
|
Positive Factors |
1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525 |
|
Negative Factors |
-1, -3, -5, -7, -15, -21, -25, -35, -75, -105, -175, -525 |
|
Prime Factors |
3, 5, 7 |
|
Prime Factorization |
31 × 52 × 71 |
This breakdown helps in understanding the various factors of 525, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 525?
There are different methods to find the factors of 525.
Methods to find the factors of 525:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 525 as their product.
Step 1: Find the pair of numbers whose product is 525.
Step 2: The factors are those numbers, when multiplied, give 525.
Step 3: Make a list of numbers whose product will be 525.
A list of numbers whose products are 525 is given below:
1 × 525 = 525
3 × 175 = 525
5 × 105 = 525
7 × 75 = 525
15 × 35 = 525
21 × 25 = 525
Thus, the factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, and 525.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 525÷1=525
Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
Thus, the factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, and 525.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using the factors of that number and expressed in the form of prime factors, is the prime factorization of a number.
Prime Factors of 525: Number 525 has three prime factors.
Prime factors of 525: 3, 5, 7
From the factors of the number 525, the prime numbers are to be selected. If the prime numbers selected can divide 525 completely, then the number is a factor of 525.
Step 1: Divide 525 with the prime number 3.
525 ÷ 3 = 175
Step 2: Divide 175 with the prime number 5.
175 ÷ 5 = 35
Step 3: Divide 35 with the prime number 7.
35 ÷ 7 = 5
Prime Factorization of 525:
Prime Factorization breaks down the prime factors of 525.
Expressed as 31 × 52 × 71.
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.
This tree shows the breakdown of 525 into its prime factors: 3 × 5 × 7.
Positive and Negative Factor Pairs of 525
Factors of 525 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
Positive Factor Pairs: (1, 525), (3, 175), (5, 105), (7, 75), (15, 35), (21, 25)
Negative Factor Pairs: (-1, -525), (-3, -175), (-5, -105), (-7, -75), (-15, -35), (-21, -25)
Common Mistakes and How to Avoid Them in Factors of 525
Mistakes can happen when finding the factors of 525. Below are some common errors and tips on how to avoid them for accurate factor identification.
Mistake 1
Thinking that 525 only has 5 as its factor.
As 525 is a multiple of 5, the students will end up thinking that 5 is the only factor of 525. Remember that factors are numbers that can divide the given number equally. 1, 3, 7, 15, 21, 25, 35, 75, 105, 175, and 525 are the factors of 525 and does not leave any remainder.
Factors of 525 Examples
Problem 1
Can you check whether 525 and 105 are co-prime?
No, 525 and 105 are not co-prime.
Explanation
To check whether the two numbers are co-prime, list their factors first.
Once you have listed the factors, identify the common factors and determine the GCF.
If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 525: 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Here, the GCF is 105. So 525 and 105 are not co-prime.
For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 525 is a multiple of 9.
No, 525 is not a multiple of 9.
Explanation
Multiples of 9 are numbers we get when 9 is multiplied by another number.
No number can be multiplied by 9 to get 525 as the product.
Problem 3
Identify the perfect square from the factors of 525.
The perfect square factor of 525 is 25 and the root is 5.
Explanation
A perfect square is a number we get when the same number is multiplied twice.
When 5 is multiplied twice (5×5), we get the perfect square 25.
Problem 4
Are 525 and 35 factors of 105?
Yes, both 525 and 35 are factors of 105.
Explanation
A factor of a number is any number that divides it exactly with no remainder.
Factors of 525: 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525
Factors of 35: 1, 5, 7, 35
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Therefore, 525 and 35 are its factors as they come in the list of factors.
Problem 5
Find the greatest common factor (GCF) of 525 and 175.
The GCF of 525 and 175 is 175.
Explanation
To find the GCF of two numbers, list their factors and identify the largest common factor.
Factors of 525: 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525
Factors of 175: 1, 5, 7, 25, 35, 175
The largest factor common to both is 175.
FAQs on Factors of 325
1.What are the factors of 525?
2.How do you determine if a number is a factor of 525?
3.What is the smallest factor of 525?
4.What is the largest factor of 525?
5.How many factors does 525 have?
6.How many odd factors does 525 have?
7.What factors go into 525?
8.Do any perfect squares exist in the factors of 525?
9.How can children in Qatar use numbers in everyday life to understand Factors of 525?
10.What are some fun ways kids in Qatar can practice Factors of 525 with numbers?
11.What role do numbers and Factors of 525 play in helping children in Qatar develop problem-solving skills?
12.How can families in Qatar create number-rich environments to improve Factors of 525 skills?
Important glossaries for the Factors of 325
Factor: The number that can divide another number completely becomes a factor for that number.
Prime Factors: The factors of a number that also come under prime numbers and when multiplied give the original number as its product.
Prime Factorization: The process of breaking down a number into its prime factors and expressing it as a product of prime numbers.
Factor Tree: A diagram used to show the breakdown of a number into its prime factors, where each branch splits into its factors.
Perfect Square: Those numbers that do not have any decimal places in the square root.
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About BrightChamps in Qatar
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.
