# Factors of 125

Factors of 125 are 1, 5, 25, and 125

#### How to find factors of a number

 1.   Find factors of 125 using Division Method 2.   Find factors of 125 using Prime Factorization 3.   Find factors of 125 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 125

• Divide 125 by 1: 125 ÷ 1 : Remainder = 0
• Divide 125 by 5: 125 ÷ 5 : Remainder = 0
• Divide 125 by 25: 125 ÷ 25 : Remainder = 0
• Divide 125 by 125: 125 ÷ 125 : Remainder = 0

Hence, Factors of 125 are 1, 5, 25, and 125

#### 2. Steps to find factors of 125 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 125 using the division method, follow these steps:

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

So, the prime factorization of 125 is, 125 = 5 x 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 125 as shown below:

So, the prime factorization of 125 is, 125 = 5 x 5 x 5.

#### 3. Find factors of 125 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 125 would be the two numbers which, when multiplied, give 125 as the result.

The following table represents the calculation of factors of 125 in pairs:

Factor Pair Pair Factorization
1 and 125 1 x 125 = 125
5 and 25 5 x 25 = 125

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 125. They are called negative pair factors.

Hence, the negative pairs of 125 would be ( -1 , -125 ) , ( -5 , -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, 5, 25, 125 are exact divisors of 125.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 125 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 125.

• What is prime factorization of 125?

Prime factorization of 125 is 5 x 5 x 5.

• How do you find factors of a negative number? ( eg. -125 )?

Factors of -125 are -1, -5, -25, -125.

• What are the prime factors of 125?

The factors of 125 are 1, 5, 25, 125.
Prime factors of 125 are 5, 5, 5.

• What are pair factors of 125?

The pair factors of 125 are (1,125), (5,25).

• What is the greatest prime factors of 125?

The greatest prime factor of 125 is 5.

• What are six multiples of 125?

First five multiples of 125 are 250, 375, 500, 625, 750, 875.

• What are factors of 125?

Factors of 125 are 1, 5, 25, 125.

• Which is the smallest prime factor of 125?

Smallest prime factor of 125 is 5.

• Is 125 a whole number?

Yes 125 is a whole number.

#### Examples of Factors

Kevin has been asked to write 3 factor(s) of 125. Can you predict the answer?

3 factor(s) of 125 are 1, 5, 25.

Sammy is puzzled while calculating the prime factors of 125. Can you help him find them?

Factors of 125 are 1, 5, 25, 125.
Prime factors of 125 are 5, 5, 5

What is prime factorization of 125?

Prime factorization of 125 is 5 x 5 x 5 = 53.

Ariel has been assigned the task to find the product of all the prime factors of 125. Can you help her?

Prime factors of 125 are 5, 5, 5.
Hence, the product of prime factors of 5.

Can you help Rubel to find out the product of the even factors of 125?

Factors of 125 are 1, 5, 25, 125.
Even factors of 125 are 0.
Hence, product of even factors of 125 is; 0 = 0.

Joy wants to calculate mean of all the factors of 125. Help him in finding the mean of 125.

Factors of 125 are 1, 5, 25, 125.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 125 is 1 + 5 + 25 + 125 = 156.
Hence, the mean of factors of 125 is 156 ÷ 4 = 39.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 125? Help her in writing all the factors.

Positive factors are 1, 5, 25, 125.
Negative factors are -1, -5, -25, -125.