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Factors of 71: Prime Factorization, Methods, and Examples

The factors of 71 are the integers that divide 71 evenly without any residue. Since it can be noted that 71 is an odd number as well as a prime number. Therefore factorization of 71 is very easy as it can only be factored as the product of 1 and 71 itself.

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.

Factors of 71

Here are the factors of number 71.

Factors of 71: 1, and 71

Negative Factors of 71

The negative factors of 71 are similar to its positive factors, just with a negative sign.

Negative Factors of 71: -1 and -71

Prime Factorization of 71

The prime factorization of 71 is the way of expressing its prime factors in the form of its product.

Prime Factorization: 1 x 71

In this article, we will learn about the factors of 71 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 71?

The factors of number 71 are 1, and 71. Both of these numbers are the factors as they do not leave any remainder when divided by 71.

The factors of 71 are classified as prime numbers as 71 itself is a prime number. The prime factors of the number 71 can be determined using the technique of prime factorization.

How To Find the Factors of 71?

You can find the factors of 71 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 71, create a list containing the numbers that are exactly divisible by 71 with zero remainders. One important thing to note is that 1 and numbers themselves are the factors of 71 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 71 are determined as follows:

\[\dfrac{71}{1} = 71\]

\[\dfrac{71}{71} = 1\]

Therefore, 1, and 71 are the factors of 71.

Total Number of Factors of 71

For 71 there are 2 positive factors as found above and 2 negative factors. So in total, there are 4 factors of 71

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

  1. Find the 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 71 is given as:

Prime Factorization of 71 is 1 x 71.

The exponent of both 1 and 71 is 1.

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

Therefore, the total number of factors of 71 is 4.

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.

Factors of 71 by Prime Factorization

The number 71 is a prime number. 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 71 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 71, 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 71 can be expressed as:

Prime Factorization of 71 = 1 x 71 

Factors of 71 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.

71 is a prime number that has only two factors therefore there can be only a 1-factor pair of 71.

For 71, the factor pair can be found as:

1 x 71 = 71

The possible factor pair of 71 is (1, 71).

Both of these numbers in pairs, when multiplied, give 71 as the product.

The negative factor pair of 71 is given as:

 -1 x -71 = 71

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, and -71 are called negative factors of 71.

The list of all the factors of number 71 including positive as well as negative numbers is given below.

Factor List of 71: 1, -1, 71, and -71 

Factors of 71 Solved Examples

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

Example 1

How many factors of 71 are there?

Solution

The total number of Factors of 71 is 4. Positive factors are 1 and 71.

Negative factors are -1 and -71.

Example 2

Find the factors of 71 using prime factorization.

Solution

The prime factorization of 71 is given as:

71 $\div$ 1 = 71 

So the prime factorization of 71 can be written as:

1 x 71 = 71

Example 3

What is the sum of factors of 71?

Solution

The sum of the factors of 71 is 1 + 71  = 72.

Therefore the sum of the factors of 71 is 72 which is an even number.

Factors of 70| Factors List |Factors of 72

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