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

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.

There are different methods to find the factors of 525.

Methods to find the factors of 525:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

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.

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.

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.

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)

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.