# Factors of 525

Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, and 525

#### How to find factors of a number

 1.   Find factors of 525 using Division Method 2.   Find factors of 525 using Prime Factorization 3.   Find factors of 525 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 525

• Divide 525 by 1: 525 ÷ 1 : Remainder = 0
• Divide 525 by 3: 525 ÷ 3 : Remainder = 0
• Divide 525 by 5: 525 ÷ 5 : Remainder = 0
• Divide 525 by 7: 525 ÷ 7 : Remainder = 0
• Divide 525 by 15: 525 ÷ 15 : Remainder = 0
• Divide 525 by 21: 525 ÷ 21 : Remainder = 0
• Divide 525 by 25: 525 ÷ 25 : Remainder = 0
• Divide 525 by 35: 525 ÷ 35 : Remainder = 0
• Divide 525 by 75: 525 ÷ 75 : Remainder = 0
• Divide 525 by 105: 525 ÷ 105 : Remainder = 0
• Divide 525 by 175: 525 ÷ 175 : Remainder = 0
• Divide 525 by 525: 525 ÷ 525 : Remainder = 0

Hence, Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, and 525

#### 2. Steps to find factors of 525 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 525 using the division method, follow these steps:

• Step 1. Start dividing 525 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 525, which is 3. Divide 525 by 3 to obtain the quotient (175).
525 ÷ 3 = 175
• Step 3. Repeat step 1 with the obtained quotient (175).
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 525 is, 525 = 3 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 525 as shown below:

So, the prime factorization of 525 is, 525 = 3 x 5 x 5 x 7.

#### 3. Find factors of 525 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 525 would be the two numbers which, when multiplied, give 525 as the result.

The following table represents the calculation of factors of 525 in pairs:

Factor Pair Pair Factorization
1 and 525 1 x 525 = 525
3 and 175 3 x 175 = 525
5 and 105 5 x 105 = 525
7 and 75 7 x 75 = 525
15 and 35 15 x 35 = 525
21 and 25 21 x 25 = 525

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 525. They are called negative pair factors.

Hence, the negative pairs of 525 would be ( -1 , -525 ) , ( -3 , -175 ) , ( -5 , -105 ) , ( -7 , -75 ) , ( -15 , -35 ) and ( -21 , -25 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525 are exact divisors of 525.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 525 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 525.

• What are the prime factors of 525?

The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.
Prime factors of 525 are 3, 5, 5, 7.

• What two numbers make 525?

Two numbers that make 525 are 3 and 175.

• What is the greatest prime factors of 525?

The greatest prime factor of 525 is 7.

• What are factors of 525?

Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.

• How do you find factors of a negative number? ( eg. -525 )?

Factors of -525 are -1, -3, -5, -7, -15, -21, -25, -35, -75, -105, -175, -525.

• What are five multiples of 525?

First five multiples of 525 are 1050, 1575, 2100, 2625, 3150.

• Write some multiples of 525?

First five multiples of 525 are 1050, 1575, 2100, 2625.

• Is 525 a perfect square?

No 525 is not a perfect square.

• What two numbers make 525?

Two numbers that make 525 are 3 and 175.

#### Examples of Factors

What is prime factorization of 525?

Prime factorization of 525 is 3 x 5 x 5 x 7 = 3 x 52 x 7.

Sammy is puzzled while calculating the prime factors of 525. Can you help him find them?

Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.
Prime factors of 525 are 3, 5, 5, 7

Kevin has been asked to write 11 factor(s) of 525. Can you predict the answer?

11 factor(s) of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175.

Joey wants to write all the prime factors of 525 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 525 are 3, 5, 5, 7.
So in exponential form it can be written as 3 x 52 x 7.

How many factors are there for 525?

Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.
So there are in total 12 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 525? Help her in writing all the factors.

Positive factors are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.
Negative factors are -1, -3, -5, -7, -15, -21, -25, -35, -75, -105, -175, -525.

Can you help Rubel to find out the product of the even factors of 525?

Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.
Even factors of 525 are 0.
Hence, product of even factors of 525 is; 0 = 0.