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Factors of 701: Prime Factorization, Methods, and Examples

In division, if the resultant is not a whole number we cannot say it is the factor of that number that is used as a divisor or in the numerator like in this solution 701. 

Only 1 and 701 satisfy the factor of 701.

Factors of 701

Here are the factors of number 701.

Factors of 701: 1 and 701

Negative Factors of 701

The negative factors of 701 are similar to its positive aspects, just with a negative sign.

Negative Factors of 701: -1 and -701

Prime Factorization of 701

The prime factorization of 701 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 701

In this article, we will learn about the factors of 701 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 701?

The factors of 701 are 1 and 701. These numbers are the factors as they do not leave any remainder when divided by 701.

The factors of 701 are classified as prime numbers and composite numbers. The prime factors of the number 701 can be determined using the prime factorization technique.

How To Find the Factors of 701?

You can find the factors of 701 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 701, create a list containing the numbers that are exactly divisible by 701 with zero remainders. One important thing to note is that 1 and 701 are the 701’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 701 are determined as follows:

\[\dfrac{701}{1} =701\]

\[\dfrac{701}{701} = 1\]

Therefore, 1 and 701 are the factors of 701.

Total Number of Factors of 701

For 701, there are two positive factors and two negative ones. So in total, there are four factors of 701. 

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 701 is given as:

Factorization of 701 is 1 x 701.

The exponent of 1 and 701 is 1.

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

Therefore, the total number of factors of 701 is four whereas two are positive, and two 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 701 by Prime Factorization

The number 701 is a prime 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 701 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 701, 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 701 can be expressed as:

701 = 1 x 701

Factors of 701 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 701, the factor pairs can be found as:

1 x 701 = 701

The possible factor pairs of 701 are given as (1, 701). 

All these numbers in pairs, when multiplied, give 701 as the product.

The negative factor pairs of 701 are given as:

-1 x -701 = 701

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 -701 are called negative factors of 701.

The list of all the factors of 701, including positive as well as negative numbers, is given below.

Factor list of 701: 1, -1, 701, and -701

Factors of 701 Solved Examples

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

Example 1

How many factors of 701 are there?

Solution

The total number of Factors of 701 is two.

Factors of 701 are 1 and 701.

Example 2

Find the factors of 701 using prime factorization.

Solution

The prime factorization of 701 is given as:

701 $\div$ 1 = 701

701 $\div$ 701 = 1 

So the prime factorization of 701 can be written as:

1 x 701 = 701

Factors of 700|Factors List| Factors of 702

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