# Factors of 25

Factors of 25 are 1, 5, and 25

#### How to find factors of a number

 1.   Find factors of 25 using Division Method 2.   Find factors of 25 using Prime Factorization 3.   Find factors of 25 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 25

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

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

#### 2. Steps to find factors of 25 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 25 using the division method, follow these steps:

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

So, the prime factorization of 25 is, 25 = 5 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 25 as shown below:

So, the prime factorization of 25 is, 25 = 5 x 5.

#### 3. Find factors of 25 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 25 would be the two numbers which, when multiplied, give 25 as the result.

The following table represents the calculation of factors of 25 in pairs:

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

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 25. They are called negative pair factors.

Hence, the negative pairs of 25 would be ( -1 , -25 ) , ( -5 , -5 ) .

#### 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 are exact divisors of 25.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 25 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 25.

• Which is the smallest prime factor of 25?

The smallest prime factor of 25 is 5.

• Is 25 a whole number?

Yes 25 is a whole number.

• What are the prime factors of 25?

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

• What two numbers make 25?

Two numbers that make 25 are 5 and 5.

• What are multiples of 25?

First five multiples of 25 are 50, 75, 100, 125.

• What is the sum of all factors of 25?

The sum of all factors of 25 is 31.

• What are five multiples of 25?

First five multiples of 25 are 50, 75, 100, 125, 150.

• Is 25 a perfect square?

Yes 25 is a perfect square.

• What is the greatest prime factors of 25?

The greatest prime factor of 25 is 5.

#### Examples of Factors

How many factors are there for 25?

Factors of 25 are 1, 5, 25.
So there are in total 3 factors.

Kevin has been asked to write 2 factor(s) of 25. Can you predict the answer?

2 factor(s) of 25 are 1, 5.

Sammy is puzzled while calculating the prime factors of 25. Can you help him find them?

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

What is prime factorization of 25?

Prime factorization of 25 is 5 x 5 = 52.

Ariel has been assigned the task to find the product of all the prime factors of 25. Can you help her?

Prime factors of 25 are 5, 5.
Hence, the product of prime factors of 5.

Can you help Rubel to find out the product of the even factors of 25?

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

Joy wants to calculate mean of all the factors of 25. Help him in finding the mean of 25.

Factors of 25 are 1, 5, 25.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 25 is 1 + 5 + 25 = 31.
Hence, the mean of factors of 25 is 31 ÷ 3 = 10.33.