# Factors of 1125

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

#### How to find factors of a number

 1.   Find factors of 1125 using Division Method 2.   Find factors of 1125 using Prime Factorization 3.   Find factors of 1125 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1125

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

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

#### 2. Steps to find factors of 1125 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 1125 using the division method, follow these steps:

• Step 1. Start dividing 1125 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 1125, which is 3. Divide 1125 by 3 to obtain the quotient (375).
1125 ÷ 3 = 375
• Step 3. Repeat step 1 with the obtained quotient (375).
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

So, the prime factorization of 1125 is, 1125 = 3 x 3 x 5 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1125 as shown below:

So, the prime factorization of 1125 is, 1125 = 3 x 3 x 5 x 5 x 5.

#### 3. Find factors of 1125 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 1125 would be the two numbers which, when multiplied, give 1125 as the result.

The following table represents the calculation of factors of 1125 in pairs:

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

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 1125. They are called negative pair factors.

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

#### 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, 1125 are exact divisors of 1125.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 1125 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1125.

• Which is the smallest prime factor of 1125?

Smallest prime factor of 1125 is 3.

• Is 1125 a perfect square?

No 1125 is not a perfect square.

• What are five multiples of 1125?

First five multiples of 1125 are 2250, 3375, 4500, 5625, 6750.

• What is prime factorization of 1125?

Prime factorization of 1125 is 3 x 3 x 5 x 5 x 5.

• What are factors of 1125?

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

• How do you find factors of a negative number? ( eg. -1125 )?

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

• Is 1125 a whole number?

Yes 1125 is a whole number.

• Which is greatest factor of 1125?

The greatest factor of 1125 is 375.

• What are the prime factors of 1125?

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

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1125. Can you help her?

Prime factors of 1125 are 3, 3, 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 1125?

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

Joy wants to calculate mean of all the factors of 1125. Help him in finding the mean of 1125.

Factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1125 is 1 + 3 + 5 + 9 + 15 + 25 + 45 + 75 + 125 + 225 + 375 + 1125 = 2028.
Hence, the mean of factors of 1125 is 2028 ÷ 12 = 169.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1125? Help her in writing all the factors.

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

How many factors are there for 1125?

Factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125.
So there are in total 12 factors.

Joey wants to write all the prime factors of 1125 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1125 are 3, 3, 5, 5, 5.
So in exponential form it can be written as 32 x 53.

Kevin has been asked to write 11 factor(s) of 1125. Can you predict the answer?

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