# Factors of 130

Factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130

#### How to find factors of a number

 1.   Find factors of 130 using Division Method 2.   Find factors of 130 using Prime Factorization 3.   Find factors of 130 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 130

• Divide 130 by 1: 130 ÷ 1 : Remainder = 0
• Divide 130 by 2: 130 ÷ 2 : Remainder = 0
• Divide 130 by 5: 130 ÷ 5 : Remainder = 0
• Divide 130 by 10: 130 ÷ 10 : Remainder = 0
• Divide 130 by 13: 130 ÷ 13 : Remainder = 0
• Divide 130 by 26: 130 ÷ 26 : Remainder = 0
• Divide 130 by 65: 130 ÷ 65 : Remainder = 0
• Divide 130 by 130: 130 ÷ 130 : Remainder = 0

Hence, Factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130

#### 2. Steps to find factors of 130 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 130 using the division method, follow these steps:

• Step 1. Start dividing 130 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 130, which is 2. Divide 130 by 2 to obtain the quotient (65).
130 ÷ 2 = 65
• Step 3. Repeat step 1 with the obtained quotient (65).
65 ÷ 5 = 13
13 ÷ 13 = 1

So, the prime factorization of 130 is, 130 = 2 x 5 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 130 as shown below:

So, the prime factorization of 130 is, 130 = 2 x 5 x 13.

#### 3. Find factors of 130 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 130 would be the two numbers which, when multiplied, give 130 as the result.

The following table represents the calculation of factors of 130 in pairs:

Factor Pair Pair Factorization
1 and 130 1 x 130 = 130
2 and 65 2 x 65 = 130
5 and 26 5 x 26 = 130
10 and 13 10 x 13 = 130

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 130. They are called negative pair factors.

Hence, the negative pairs of 130 would be ( -1 , -130 ) , ( -2 , -65 ) , ( -5 , -26 ) and ( -10 , -13 ) .

#### 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

• Each number is a factor of itself. Eg. 130 is a factor of itself.
• 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, 2, 5, 10, 13, 26, 65, 130 are exact divisors of 130.
• 1 is a factor of every number. Eg. 1 is a factor of 130.
• Every number is a factor of zero (0), since 130 x 0 = 0.

• Is 130 a perfect square?

No 130 is not a perfect square.

• What are factors of 130?

Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130.

• Which is greatest factor of 130?

The greatest factor of 130 is 65.

• What is the sum of all factors of 130?

The sum of all factors of 130 is 252.

• What are multiples of 130?

First five multiples of 130 are 260, 390, 520, 650.

• What is the greatest prime factors of 130?

The greatest prime factor of 130 is 13.

• What are six multiples of 130?

First five multiples of 130 are 260, 390, 520, 650, 780, 910.

• What is prime factorization of 130?

Prime factorization of 130 is 2 x 5 x 13.

• Is 130 a whole number?

Yes 130 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 130? Help her in writing all the factors.

Positive factors are 1, 2, 5, 10, 13, 26, 65, 130.
Negative factors are -1, -2, -5, -10, -13, -26, -65, -130.

Can you help Sammy find out the product of the odd factors of 130?

Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130.
Odd factors of 130 are 1, 5, 13, 65.
Hence product of odd factors of 130 is; 1 x 5 x 13 x 65 = 4225.

Joey wants to write all the prime factors of 130 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 130 are 2, 5, 13.
So in exponential form it can be written as 2 x 5 x 13.

How many factors are there for 130?

Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 130. Can you predict the answer?

7 factor(s) of 130 are 1, 2, 5, 10, 13, 26, 65.

Sammy is puzzled while calculating the prime factors of 130. Can you help him find them?

Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130.
Prime factors of 130 are 2, 5, 13

What is prime factorization of 130?

Prime factorization of 130 is 2 x 5 x 13 = 2 x 5 x 13.