Factors of 65 | Prime Factorization of 65 | Factor Tree of 65

The numbers that divide a given number thoroughly and evenly without leaving any remainder are known as the factors of that number. A number can have both positive and negative factors. In this article, you will learn about factors of 65 using the factor tree method, prime factorization method, and division method.

What Are the Factors of 65?

The numbers that can divide the given number 65 without leaving behind any reminder are known as the factors of the given number 65. A number can have both negative and positive factors. Apart from that, the factors can also be categorized as prime numbers and composite numbers. Composite numbers are numbers that have more than two factors while prime numbers are numbers that have two or less than two numbers as factors. Thus, 65 is a composite number as it has more than two factors. And the factors of 65 are 1, 5, 13, and 65.

Factors of 65: 1, 5, 13, and 65.

Negative Factors of 65: -1, -5, -13, and -65.

Prime Factorization of 65: 5 x 13

Pair Factors of 65: (5, 13), (1, 65)

Prime Factors of 65: 5 and 13

Sum of Factors of 65: 84

Sum of Prime Factors of 65: 18

Factors of 65

What are the Factors of 65 in Pairs?

The number 65 has both positive and negative factors. The combination of two numbers is called a pair factor of 65. When we multiply the pair factors of 65, the result will always be 65 and we will always get the original product.

Positive Pair Factors of 65

The positive pair factors of 65 are: (5, 13), (1, 65).

Negative Pair Factors of 65

The negative pair factors are: (-5, -13), (-1, -65).

What Is the Factor Tree of 65?

The prime factors of 65 can also be found using the factor tree method. For this purpose, place 65 at the top of the factor tree. Then split the numbers into their factors and then write the set of the pair factors. This process should be continued till the factors turn into prime numbers. And so finally by identifying all the prime numbers we will get a prime factor of 65. The steps involved in this process are given below:

Step 1: Let’s place the number 65 at the top and write down 65 in pairs, that is, 5, 13.
Step 2: And now the branches in the factor tree are prime numbers. So, it’s not possible to write the pairs more, hence let’s stop here.
Circling all the branches, 5 x 13, which are the prime factors of 65.
There are many ways in which we can write the factor tree of 65. Below is an image representation of the factor tree of 65, choosing 5 and 13 as pair factors of 65.

How To Find Factors of 65 Through Division Method?

Any numbers that divide 65 without leaving any remainder are known as factors of 65. Through the division method, we can find the factors of 92 by a dividing sequence of numbers. The steps are mentioned below for a better understanding of it:

65 ÷ 1 = 65
65 ÷ 5 = 13
65 ÷ 13 = 5
65 ÷ 65 = 1

Therefore, the factors of 65 are 1, 5, 13, and 65.

Prime Factorization of 65

Prime factorization is a method used to find the prime factors of a number. Before doing the prime factorization method, it’s important to check whether the given number is a prime number or a composite number. Here, 65 is a composite number as it has more than two factors. The steps involved in the prime factorization method are given below:

Step 1: Let’s place the number 65 at the top and write down 65 in pairs, that is, 5 and 13.
Step 2: We get 13 as the quotient. As 13 is a prime number, we cannot divide it further and so it is divisible by itself. That is 13 ÷ 13 = 1. Circling all the branches, 1 x 5 x 13 which are the prime factors of 65.

There are many ways in which we can write the factor tree of 65. Below is an image representation of the factor tree of 65, choosing 5 and 13 as pair factors of 65.