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Factors of 86: Prime Factorization, Methods, and Examples

The factors of number 86 can be classified as the group of numbers that when divided by 86 result in a whole number with nothing as a remainder. 86 is a composite number therefore it has more than two factors.

The factors of the given number can be positive and negative provided that the product of any of those two is always the factored number. Let’s further elaborate on the concept of factors of 86 and how to find the factors of 86.

Factors of 86

Here are the factors of number 86.

Factors of 86: 1, 2, 43, and 86

Negative Factors of 86

The negative factors of 86 are similar to its positive factors, just with a negative sign.

Negative Factors of 86: -1, -2, -43 and -86 

Prime Factorization of 86

The prime factorization of 86 is the way of expressing a number’s prime factors in the form of its product.

Prime Factorization of 86: 2 x 43

In this article, we will learn about the factors of 86 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 86?

The factors of number 86 are 1, 2, 43, and 86. All of these numbers are the factors as they do not leave any remainder when divided by 86.

The factors of number 86 are classified as prime numbers and composite numbers. The prime factors of the number 86 can be determined using the technique of prime factorization.

How To Find the Factors of 86?

You can find the factors of 86 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 86, create a list containing the numbers that are exactly divisible by 86 with zero remainders. One important thing to note is that 1 and 86 are the factors of the 86 as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 86 are determined as follows:

\[\dfrac{86}{1} = 86\]

\[\dfrac{86}{2} = 43\]

\[\dfrac{86}{43} = 2\]

\[\dfrac{86}{86} = 1\]

Therefore, 1, 2, 43, and 86 are the factors of 86.

Total Number of Factors of 86

For 86 there are 4 positive factors as found above and 4 negative factors. So in total, there are 8 factors of 86. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure the total number of factors of 86 is given as:

Factorization of 86 is 1 x 2 x 43.

The exponent of all the factors is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 86 is 8.

Important Notes

Here are some important points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor which is the smallest prime factor.
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Factors of 86 by Prime Factorization

The number 86 is composite. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 86 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 86, start dividing by its smallest prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 86 can be expressed as:

 86 = 2 x 43 

Factors of 86 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.

For 86, the factor pairs can be found as:

1 x 86 = 86 

2 x 43 = 86

The possible factor pairs of 86 are (1, 86) and (2, 43 ).

All these numbers in pairs, when multiplied, give 86 as the product.

The negative factor pairs of 86 are given as:

 -1 x -86 = 86

-2 x -43 = 86

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign due to which the resulting product is the original positive number. Therefore, -1, -2, -43, and -86 are called negative factors of 86.

The list of all the factors of 86 including positive as well as negative numbers is given below.

Factor List of 86: 1, -1, 2, -2, 43, -43, 86, and -86

Factors of 86 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 86 are there?

Solution

The total number of Factors of 86 is 8.

Example 2

Find the factors of 86 using prime factorization.

Solution

The prime factorization of 86 is given as:

86 $\div$ 2 = 43 

43 $\div$ 43 = 1 

So the prime factorization of 86 can be written as:

2 x 43 = 86

Factors of 85|Factors List |Factors of 87

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