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Factors of 671: Prime Factorization, Methods, and Examples

671 is the number having four factors that are used as divisors to give positive integer numbers without decimal places. 

For instance, Factors 1, 11, 61, and 671 are used as divisors then give 671, 61, 11, and 1 as quotients respectively.

Factors of 671

Here are the factors of number 671.

Factors of 671: 1, 11, 61, and 671

Negative Factors of 671

The negative factors of 671 are similar to its positive aspects, just with a negative sign.

Negative Factors of 671: -1, -11, -61, and -671

Prime Factorization of 671

The prime factorization of 671 is the way of expressing its prime factors in the product form.

Prime Factorization: 11 x 61

In this article, we will learn about the factors of 671 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 671?

The factors of 671 are 1, 11, 61, and 671. These numbers are the factors as they do not leave any remainder when divided by 671.

The factors of 671 are classified as prime numbers and composite numbers. The prime factors of the number 671 can be determined using the prime factorization technique.

How To Find the Factors of 671?

You can find the factors of 671 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 671, create a list containing the numbers that are exactly divisible by 671 with zero remainders. One important thing to note is that 1 and 671 are the 671’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 671 are determined as follows:

\[\dfrac{671}{1} = 671\]

\[\dfrac{671}{11} = 61\]

\[\dfrac{671}{61} = 11\]

\[\dfrac{671}{671} = 1\]

Therefore, 1, 11, 61, and 671 are the factors of 671.

Total Number of Factors of 671

For 671, there are four positive factors and four negative ones. So in total, there are eight factors of 671. 

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 671 is given as:

Factorization of 671 is 11 x 61

The exponent of 11 and 61 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 671 is eight whereas four are positive, and four 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 671 by Prime Factorization

The number 671 is a composite. 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 671 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 671, 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 671 can be expressed as:

671 = 11 x 61

Factors of 671 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 671, the factor pairs can be found as:

1 x 671 = 671

11 x 61 = 671 

The possible factor pairs of 671 are given as (1, 671) and (11, 61 ).

All these numbers in pairs, when multiplied, give 671 as the product.

The negative factor pairs of 671 are given as:

-1 x -671 = 671

-11 x -61 = 671 

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, -11, -61, and -671 are called negative factors of 671.

The list of all the factors of 671, including positive as well as negative numbers, is given below.

Factor list of 671: 1, -1, 11, -11, 61, -61, 671 and -671

Factors of 671 Solved Examples

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

Example 1

How many factors of 671 are there?

Solution

The total number of Factors of 671 is four.

Factors of 671 are 1, 11, 61, and 671.

Example 2

Find the factors of 671 using prime factorization.

Solution

The prime factorization of 671 is given as:

671 $\div$ 11 = 61 

61 $\div$ 11 = 1 

So the prime factorization of 671 can be written as:

11 x 61 = 671

Factors of 670|Factors List| Factors of 672

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