# Factors of 725

Factors of 725 are 1, 5, 25, 29, 145, and 725

#### How to find factors of a number

 1.   Find factors of 725 using Division Method 2.   Find factors of 725 using Prime Factorization 3.   Find factors of 725 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 725

• Divide 725 by 1: 725 ÷ 1 : Remainder = 0
• Divide 725 by 5: 725 ÷ 5 : Remainder = 0
• Divide 725 by 25: 725 ÷ 25 : Remainder = 0
• Divide 725 by 29: 725 ÷ 29 : Remainder = 0
• Divide 725 by 145: 725 ÷ 145 : Remainder = 0
• Divide 725 by 725: 725 ÷ 725 : Remainder = 0

Hence, Factors of 725 are 1, 5, 25, 29, 145, and 725

#### 2. Steps to find factors of 725 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 725 using the division method, follow these steps:

• Step 1. Start dividing 725 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 725, which is 5. Divide 725 by 5 to obtain the quotient (145).
725 ÷ 5 = 145
• Step 3. Repeat step 1 with the obtained quotient (145).
145 ÷ 5 = 29
29 ÷ 29 = 1

So, the prime factorization of 725 is, 725 = 5 x 5 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 725 as shown below:

So, the prime factorization of 725 is, 725 = 5 x 5 x 29.

#### 3. Find factors of 725 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 725 would be the two numbers which, when multiplied, give 725 as the result.

The following table represents the calculation of factors of 725 in pairs:

Factor Pair Pair Factorization
1 and 725 1 x 725 = 725
5 and 145 5 x 145 = 725
25 and 29 25 x 29 = 725

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 725. They are called negative pair factors.

Hence, the negative pairs of 725 would be ( -1 , -725 ) , ( -5 , -145 ) and ( -25 , -29 ) .

#### 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, 29, 145, 725 are exact divisors of 725.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 725 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 725.

• What are the pair factors of 725?

Pair factors of 725 are (1,725), (5,145), (25,29).

• What are five multiples of 725?

First five multiples of 725 are 1450, 2175, 2900, 3625, 4350.

• What two numbers make 725?

Two numbers that make 725 are 5 and 145.

• What is the sum of all factors of 725?

The sum of all factors of 725 is 930.

• What are factors of -725?

Factors of -725 are -1, -5, -25, -29, -145, -725.

• What are factors of 725?

Factors of 725 are 1, 5, 25, 29, 145, 725.

• Is 725 a perfect square?

No 725 is not a perfect square.

• Which is the smallest prime factor of 725?

Smallest prime factor of 725 is 5.

• Which is greatest factor of 725?

The greatest factor of 725 is 145.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 725?

Factors of 725 are 1, 5, 25, 29, 145, 725.
Odd factors of 725 are 1, 5, 25, 29, 145, 725.
Hence product of odd factors of 725 is; 1 x 5 x 25 x 29 x 145 x 725 = 381078125.

Joey wants to write all the prime factors of 725 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 725 are 5, 5, 29.
So in exponential form it can be written as 52 x 29.

How many factors are there for 725?

Factors of 725 are 1, 5, 25, 29, 145, 725.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 725. Can you predict the answer?

5 factor(s) of 725 are 1, 5, 25, 29, 145.

Sammy is puzzled while calculating the prime factors of 725. Can you help him find them?

Factors of 725 are 1, 5, 25, 29, 145, 725.
Prime factors of 725 are 5, 5, 29

What is prime factorization of 725?

Prime factorization of 725 is 5 x 5 x 29 = 52 x 29.

Can you help Rubel to find out the product of the even factors of 725?

Factors of 725 are 1, 5, 25, 29, 145, 725.
Even factors of 725 are 0.
Hence, product of even factors of 725 is; 0 = 0.