Factors of 847: Prime Factorization, Methods, and Examples

847 has four factors that are positive and four that are negative. These factors are  1, 7, 11, 77, 121, and 847, which are equally divided by 847 to provide a quotient with no decimal places.

 Because this number has four positive elements that add up to more than two, we say it is composite.

Factors of 847

Here are the factors of number 847.

Factors of 847: 1, 7, 11, 77, 121 and 847

Negative Factors of 847

The negative factors of 847  are similar to its positive aspects, just with a negative sign.

Negative Factors of 847: -1, -7, -11, -77, -121 and -847

Prime Factorization of 847

The prime factorization of 847  is the way of expressing its prime factors in the product form.

Prime Factorization: 7¹ x 11²

In this article, we will learn about the factors of 847 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 847?

The factors of 847  are 1, 7, 11, 77, 121, and 847. These numbers are the factors as they do not leave any remainder when divided by 847.

The factors of 847 are classified as prime numbers and composite numbers. The prime factors of the number 847 can be determined using the prime factorization technique.

How To Find the Factors of 847?

You can find the factors of 847 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 847, create a list containing the numbers that are exactly divisible by 847 with zero remainders. One important thing to note is that 1 and 847 are the 847’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 847 are determined as follows:

\[\dfrac{847}{1} = 847\]

\[\dfrac{847}{7} = 121\]

\[\dfrac{847}{11} = 77\]

\[\dfrac{847}{77} = 11\]

\[\dfrac{847}{121} = 7\]

\[\dfrac{847}{847} = 1\]

Therefore, 1, 7, 11, 77, 121, and 847 are the factors of 847.

Total Number of Factors of 847

For 847, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 847. 

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 847 is given as:

Factorization of 847 is 1 x 7¹ × 11².

The exponent of 1 is 1, 7 is 1, and 11 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 847 is 12. 6 are positive, and 6 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 847 by Prime Factorization

The number 847 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 847 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 847, 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 847 can be expressed as:

847 = 7¹ x 11²

Factors of 847 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 847, the factor pairs can be found as:

1 x 847 = 847

7 x 121 = 847

11 x 77 = 847

The possible factor pairs of 847 are given as (1, 847), (7, 121), and (11, 77).

All these numbers in pairs, when multiplied, give 847 as the product.

The negative factor pairs of 847 are given as:

-1 x -847 = 847

-7 x -121 = 847

-11 x -77 = 847

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, -7, -11, -77, -121 and -847 are called negative factors of 847.

The list of all the factors of 847, including positive as well as negative numbers, is given below.

Factor list of 847: 1,-1, 7,-7, 11,-11, 77,-77, 121,-121 , 847, and -847

Factors of 847 Solved Examples

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

Example 1

How many factors of 847 are there?

Solution

The total number of Factors of 847 is 12.

Factors of 847 are 1, 7, 11, 77, 121, and 847.

Example 2

Find the factors of 847 using prime factorization.

Solution

The prime factorization of 847 is given as:

847 $\div$ 7 = 121 

121 $\div$ 11 = 11 

11 $\div$ 11 = 1 

So the prime factorization of 847 can be written as:

7¹ x 11² = 847

Factors of 846|Factors List| Factors of 848