# Factors of 5625

Factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, and 5625

#### How to find factors of a number

 1.   Find factors of 5625 using Division Method 2.   Find factors of 5625 using Prime Factorization 3.   Find factors of 5625 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 5625

• Divide 5625 by 1: 5625 ÷ 1 : Remainder = 0
• Divide 5625 by 3: 5625 ÷ 3 : Remainder = 0
• Divide 5625 by 5: 5625 ÷ 5 : Remainder = 0
• Divide 5625 by 9: 5625 ÷ 9 : Remainder = 0
• Divide 5625 by 15: 5625 ÷ 15 : Remainder = 0
• Divide 5625 by 25: 5625 ÷ 25 : Remainder = 0
• Divide 5625 by 45: 5625 ÷ 45 : Remainder = 0
• Divide 5625 by 75: 5625 ÷ 75 : Remainder = 0
• Divide 5625 by 125: 5625 ÷ 125 : Remainder = 0
• Divide 5625 by 225: 5625 ÷ 225 : Remainder = 0
• Divide 5625 by 375: 5625 ÷ 375 : Remainder = 0
• Divide 5625 by 625: 5625 ÷ 625 : Remainder = 0
• Divide 5625 by 1125: 5625 ÷ 1125 : Remainder = 0
• Divide 5625 by 1875: 5625 ÷ 1875 : Remainder = 0
• Divide 5625 by 5625: 5625 ÷ 5625 : Remainder = 0

Hence, Factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, and 5625

#### 2. Steps to find factors of 5625 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 5625 using the division method, follow these steps:

• Step 1. Start dividing 5625 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 5625, which is 3. Divide 5625 by 3 to obtain the quotient (1875).
5625 ÷ 3 = 1875
• Step 3. Repeat step 1 with the obtained quotient (1875).
1875 ÷ 3 = 625
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 5625 is, 5625 = 3 x 3 x 5 x 5 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 5625 as shown below:

So, the prime factorization of 5625 is, 5625 = 3 x 3 x 5 x 5 x 5 x 5.

#### 3. Find factors of 5625 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 5625 would be the two numbers which, when multiplied, give 5625 as the result.

The following table represents the calculation of factors of 5625 in pairs:

Factor Pair Pair Factorization
1 and 5625 1 x 5625 = 5625
3 and 1875 3 x 1875 = 5625
5 and 1125 5 x 1125 = 5625
9 and 625 9 x 625 = 5625
15 and 375 15 x 375 = 5625
25 and 225 25 x 225 = 5625
45 and 125 45 x 125 = 5625
75 and 75 75 x 75 = 5625

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 5625. They are called negative pair factors.

Hence, the negative pairs of 5625 would be ( -1 , -5625 ) , ( -3 , -1875 ) , ( -5 , -1125 ) , ( -9 , -625 ) , ( -15 , -375 ) , ( -25 , -225 ) , ( -45 , -125 ) and ( -75 , -75 ) .

#### 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, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625 are exact divisors of 5625.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 5625 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 5625.

• Which is the smallest prime factor of 5625?

Smallest prime factor of 5625 is 3.

• Is 5625 a perfect square?

Yes 5625 is a perfect square.

• What are five multiples of 5625?

First five multiples of 5625 are 11250, 16875, 22500, 28125, 33750.

• What is prime factorization of 5625?

Prime factorization of 5625 is 3 x 3 x 5 x 5 x 5 x 5.

• What are factors of 5625?

Factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625.

• How do you find factors of a negative number? ( eg. -5625 )?

Factors of -5625 are -1, -3, -5, -9, -15, -25, -45, -75, -125, -225, -375, -625, -1125, -1875, -5625.

• Is 5625 a whole number?

Yes 5625 is a whole number.

• Which is greatest factor of 5625?

The greatest factor of 5625 is 1875.

• What are the prime factors of 5625?

The factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625.
Prime factors of 5625 are 3, 3, 5, 5, 5, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 5625. Can you help her?

Prime factors of 5625 are 3, 3, 5, 5, 5, 5.
Hence, the product of prime factors of 15.

Can you help Rubel to find out the product of the even factors of 5625?

Factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625.
Even factors of 5625 are 0.
Hence, product of even factors of 5625 is; 0 = 0.

Joy wants to calculate mean of all the factors of 5625. Help him in finding the mean of 5625.

Factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 5625 is 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 + 125 + 225 + 375 + 625 + 1125 + 1875 + 5625 = 10153.
Hence, the mean of factors of 5625 is 10153 ÷ 15 = 676.87.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 5625? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625.
Negative factors are -1, -3, -5, -9, -15, -25, -45, -75, -125, -225, -375, -625, -1125, -1875, -5625.

How many factors are there for 5625?

Factors of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875, 5625.
So there are in total 15 factors.

Joey wants to write all the prime factors of 5625 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 5625 are 3, 3, 5, 5, 5, 5.
So in exponential form it can be written as 32 x 54.

Kevin has been asked to write 14 factor(s) of 5625. Can you predict the answer?

14 factor(s) of 5625 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875.