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Factors of 858: Prime Factorization, Methods, and Examples

The factors of 858 are numbers that, when divided by 858, leave zero as the remainder. The given number’s factors can be positive and negative. 

Let us explore more about factors of 858 in this article.

Factors of 858

Here are the factors of number 858.

Factors of 858: 1 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, and 858.

Negative Factors of 858

The negative factors of 858 are similar to its positive aspects, just with a negative sign.

Negative Factors of 858: –1 -2, -3, -6, -11, -13, -22, -26, -33, -39, -66, -78, -143, -286, -429, and -858

Prime Factorization of 858

The prime factorization of 858 is the way of expressing its prime factors in the product form.

 

Prime Factorization: 2 x 3 x 11 x 13

In this article, we will learn about the factors of 858 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 858?

The factors of 858 are 1 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, and 858. These numbers are the factors as they do not leave any remainder when divided by 858.

The factors of 858 are classified as prime numbers and composite numbers. The prime factors of the number 858 can be determined using the prime factorization technique.

How To Find the Factors of 858?

You can find the factors of 858 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, 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 858, create a list containing the numbers that are exactly divisible by 858 with zero remainders. One important thing to note is that 1 and 858 are the 858’s factors 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 858 are determined as follows:

\[\dfrac{858}{1} = 858\]

\[\dfrac{858}{2} = 429\]

\[\dfrac{858}{3} = 286\]

\[\dfrac{858}{6} = 143\]

\[\dfrac{858}{11} = 78\]

\[\dfrac{858}{13} = 66\]

\[\dfrac{858}{22} = 39\]

\[\dfrac{858}{26} = 33\]

Therefore, 1 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, and 858 are the factors of 858.

Total Number of Factors of 858

For 858, there are sixteen positive factors and sixteen negative ones. So in total, there are 32 factors of 858. 

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

  1. Find the factorization/prime 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 prime 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 858 is given as:

Factorization of 858 is 1 x 2 x 3 x 11 x 13.

The exponent of 1, 2, 3, 11, and 13 is 1.

Adding 1 to each and multiplying them together results in 32.

Therefore, the total number of factors of 858 is 32. Sixteen are positive, and sixteen factors are negative.

Important Notes

Here are some essential 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, the smallest prime factor.

Factors of 858 by Prime Factorization

The number 858 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 858 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 858, start dividing by its most minor 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 858 can be expressed as:

858 = 2 x 3 x 11 x 13

Factors of 858 in Pairs

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

 

 

For 858, the factor pairs can be found as:

1 x 858 = 858

2 x 429 = 858

3 x 286 = 858

6 x 143 = 858

11 x 78 = 858

13 x 66 = 858

22 x 39 = 858

26 x 33 = 858

The possible factor pairs of 858 are given as (1, 858), (2, 429), (3, 286), (6, 143), (11, 78), (13, 66), (22, 39) and (26, 33).

All these numbers in pairs, when multiplied, give 858 as the product.

The negative factor pairs of 858 are given as:

1 x -858 = 858

-2 x -429 = 858

-3 x -286 = 858

-6 x -143 = 858

-11 x -78 = 858

-13 x -66 = 858

-22 x -39 = 858

-26 x -33 = 858

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, -3, -6, -11, -13, -22, -26, -33, -39, -66, -78, -143, -286, -429, and -858 are called negative factors of 858.

The list of all the factors of 858, including positive as well as negative numbers, is given below.

Factor list of 858: 1, -1, 2, -2, 3, -3, 6, -6, 11, -11, 13, -13, 22, -22, 26, -26, 33, -33, 39, -39, 66, -66, 78, -78, 143, -143, 286, -286, 429, -429, 858, and -858

Factors of 858 Solved Examples

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

Example 1

How many factors of 858 are there?

Solution

The total number of Factors of 858 is 32.

Factors of 858 are 1 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, and 858.

Example 2

Find the factors of 858 using prime factorization.

Solution

The prime factorization of 858 is given as:

858 $\div$ 2 = 429 

429 $\div$ 3 = 143

143 $\div$ 11 = 13

13 $\div$ 13 = 1 

So the prime factorization of 858 can be written as:

2 x 3 x 11 x 13 = 858

Factors of 857|Factors List| Factors of 859

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