# Factors of 259

Factors of 259 are 1, 7, 37, and 259

#### How to find factors of a number

 1.   Find factors of 259 using Division Method 2.   Find factors of 259 using Prime Factorization 3.   Find factors of 259 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 259

• Divide 259 by 1: 259 ÷ 1 : Remainder = 0
• Divide 259 by 7: 259 ÷ 7 : Remainder = 0
• Divide 259 by 37: 259 ÷ 37 : Remainder = 0
• Divide 259 by 259: 259 ÷ 259 : Remainder = 0

Hence, Factors of 259 are 1, 7, 37, and 259

#### 2. Steps to find factors of 259 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 259 using the division method, follow these steps:

• Step 1. Start dividing 259 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 259, which is 7. Divide 259 by 7 to obtain the quotient (37).
259 ÷ 7 = 37
• Step 3. Repeat step 1 with the obtained quotient (37).
37 ÷ 37 = 1

So, the prime factorization of 259 is, 259 = 7 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 259 as shown below:

So, the prime factorization of 259 is, 259 = 7 x 37.

#### 3. Find factors of 259 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 259 would be the two numbers which, when multiplied, give 259 as the result.

The following table represents the calculation of factors of 259 in pairs:

Factor Pair Pair Factorization
1 and 259 1 x 259 = 259
7 and 37 7 x 37 = 259

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 259. They are called negative pair factors.

Hence, the negative pairs of 259 would be ( -1 , -259 ) , ( -7 , -37 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every number is a factor of zero (0), since 259 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 7, 37, 259 are exact divisors of 259.
• Factors of 259 are 1, 7, 37, 259. Each factor divides 259 without leaving a remainder.

• Which is the smallest prime factor of 259?

The smallest prime factor of 259 is 7.

• Is 259 a whole number?

Yes 259 is a whole number.

• What are the prime factors of 259?

The factors of 259 are 1, 7, 37, 259.
Prime factors of 259 are 7, 37.

• What two numbers make 259?

Two numbers that make 259 are 7 and 37.

• What are multiples of 259?

First five multiples of 259 are 518, 777, 1036, 1295.

• What is the sum of all factors of 259?

The sum of all factors of 259 is 304.

• What are five multiples of 259?

First five multiples of 259 are 518, 777, 1036, 1295, 1554.

• Is 259 a perfect square?

No 259 is not a perfect square.

• What is the greatest prime factors of 259?

The greatest prime factor of 259 is 37.

#### Examples of Factors

How many factors are there for 259?

Factors of 259 are 1, 7, 37, 259.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 259. Can you predict the answer?

3 factor(s) of 259 are 1, 7, 37.

Sammy is puzzled while calculating the prime factors of 259. Can you help him find them?

Factors of 259 are 1, 7, 37, 259.
Prime factors of 259 are 7, 37

What is prime factorization of 259?

Prime factorization of 259 is 7 x 37 = 7 x 37.

Ariel has been assigned the task to find the product of all the prime factors of 259. Can you help her?

Prime factors of 259 are 7, 37.
Hence, the product of prime factors of 259.

Can you help Rubel to find out the product of the even factors of 259?

Factors of 259 are 1, 7, 37, 259.
Even factors of 259 are 0.
Hence, product of even factors of 259 is; 0 = 0.

Joy wants to calculate mean of all the factors of 259. Help him in finding the mean of 259.

Factors of 259 are 1, 7, 37, 259.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 259 is 1 + 7 + 37 + 259 = 304.
Hence, the mean of factors of 259 is 304 ÷ 4 = 76.00.