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Factors of 85 | Prime Factorization of 85 | Factor Tree of 85

Written by Prerit Jain

Updated on: 15 Feb 2023

Factors of 85 | Prime Factorization of 85 | Factor Tree of 85

Factors of 85 | Prime Factorization of 85 | Factor Tree of 85

In Mathematics, the factors of a number are the numbers that, on multiplying with each other, result in a given number. The factors of a number can be classified as prime numbers and composite numbers. Prime numbers have two or less than two numbers as their factors, while composite numbers have more than two factors. 

What Are the Factors of 85?

The numbers that can divide the number 85 uniformly with zero remainders are known as the factors of 85. The number 85 is a composite number as it has more than two factors and they are 1, 5, 17, and 85.

Factors of 85: 1, 5, 17, and 85.
Negative Factors of 85: -1, -5, -17, and -85.
Prime Factorization of 85: 5 x 17
Pair Factors of 85: (1, 85) and (5, 17)
Prime Factors of 85: 5 and 17
Sum of Factors of 85: 108
Sum of Prime Factors of 85: 22
Factors of 85

What Are the Factors of 85 in Pairs?

The pair factors of the number 85 are the numbers which on multiplying with each other produce the number 85. There exist both negative and positive pair factors for a number.

Positive Pair Factors of 85

The positive pair factors of 85 are (1, 85) and (5, 17).

Positive Pair Factors of 85

Negative Pair Factors of 85

The negative pair factors of 85 are (-1, -85) and (-5, -17).

Negative Pair Factors of 85

Factorization of 85

The process of finding the factors of the number 85 is known as the factorization of 85. It can be found by using 3 methods and they are:

  • Basic prime factorization Method
  • Division Method
  • Factor Tree Method

What Is the Prime Factorization Method of 85?

Through the basic prime factorization method, we can find the prime factors of 85. The steps are as follows:

  • Step 1: Place the number 85 at the top. Let’s divide 85 by the smallest number that can divide that number and that is 5.
    85 ÷ 5 = 17
  • Step 2: The number 17 is not further divisible by another number and so it’s divisible by itself only.
    17 ÷ 17 = 1
  • Step 3: We have got the remainder as 1. Therefore, the prime factors of 85 are 5 and 17.

The below image shows the basic prime factorization of 85.

Prime Factorization of 85

How to Find Factors of 85 Through Division Method?

In the division method, the given number 85 will be divided by the smallest prime numbers and again the remainder obtained will be divided by the smallest number that can divide it. And this process will be continued till the remainder becomes 1. The steps are as follows:

  • 85 ÷ 1= 85
  • 85 ÷ 5 = 17
  • 85 ÷ 17 = 5
  • 85 ÷ 85 = 1

Therefore, the factors of 85 are 1, 5, 17, and 85.

What Is the Factor Tree of 85?

A factor tree is another method, with which we can find the prime factors of 85. In the factor tree method, only the composite numbers will be having branches and not the prime numbers that can divide the given number 85. The steps involved in the process are as follows:

  • Step 1: Place the number 85 at the top of the factor tree and write the first set of pair factors on its branches and they are 5 and 17.
  • Step 2: The numbers 5 and 17 are not further divisible by other numbers. So the prime factor of 85 is 5 x 17.

The below image shows the factor tree of 85.

Factor tree of 85

Solved Examples of 85

What are the factors of 85?
The factors of 85 are 1, 5, 17, and 85.

What is the sum of the factors of 85?
The sum of the factors of 85 is 108

What are the pair factors of 85?
The pair factors of 85 are (1, 85) and (5, 17).

What are the negative factors of 85?
The negative factors of 85 are -1, -5, -17, and -85.

Frequently Asked Questions

What are the divisors of 85?
The divisors of 85 are its factors itself and they are 1, 5, 17, and 85.

Why is 85 a prime number?
85 is not a prime number, as it has more than two numbers as its factors. They are 1, 5, 17, and 85.

How do you divide 85 evenly?
The number 85 is divided evenly by its factors and they are 1, 5, 17, and 85.

Is 85 a perfect cube?
No, the number 85 is not a perfect cube as there is a decimal point in its quotient. The cube root of 85 is 4.39682967216.

What is the root of 85?
The square root of 85 is 9.21954445729.

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Prerit Jain

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