Factors of 201: Prime Factorization, Methods, and Examples

The factors of 201 are the numbers that give off zero as the remainder when 201 is divided from them. These divisors also produce a whole number quotient; hence, both the divisor and the quotient act as factors. They also form a factor pair. 

Factors Of 201

These factors can be both positive and negative.  

Factors of 201

Here are the factors of number 201.

Factors of 201: 1, 3, 67, 201

Negative Factors of 201

The negative factors of 201 are similar to its positive factors, just with a negative sign.

Negative Factors of 201: -1, -3, -67, and -201

Prime Factorization of 201

The prime factorization of 201 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 67

In this article, we will learn about the factors of 201 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 201?

The factors of 201 are 1, 3, 67, and 201. All of these numbers are the factors as they do not leave any remainder when divided by 201.

The factors of 201 are classified as prime numbers and composite numbers. The prime factors of the number 201 can be determined using the prime factorization technique.

How To Find the Factors of 201?

You can find the factors of 201 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 201, create a list containing the numbers that are exactly divisible by 201 with zero remainders. One important thing to note is that 1 and 201 are the 201’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 201 are determined as follows:

\[\dfrac{201}{1} = 201\]

\[\dfrac{201}{3} = 67\]

\[\dfrac{201}{67} = 3\]

\[\dfrac{201}{201} = 1\]

Therefore, 1, 3, 67, and 201 are the factors of 201.

Total Number of Factors of 201

For 201, there are four positive factors and four negative ones. So in total, there are eight factors of 201. 

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

  1. Find the 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 201 is given as:

Factorization of 201 is 1 x 3 x 67.

The exponent of 1, 3, and 67 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 201 is 8. 4 are positive, and four factors are negative.

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, the smallest prime factor.

Factors of 201 by Prime FactorizationFactor of 201 by Prime Factorization

The number 201 is a composite 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 201 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 201, 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 201 can be expressed as:

201 = 3 x 67

Factors of 201 in PairsFactor of 201 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 of the given numbers.

For 201, the factor pairs can be found as:

 1 x 201 = 201 

3 x 67 = 201 

The possible factor pairs of 201 are (1, 201) and (3, 67).

All these numbers in pairs, when multiplied, give 201 as the product.

The negative factor pairs of 201 are given as:

-1 x -201 = 201 

-1 x -67 = 201

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, -3, -67, and -201 are called negative factors of 201.

The list of all the factors of 201, including positive as well as negative numbers, is given below.

Factor list of 201: 1, -1, 3, -3, 67, -67, 201, and -201

Factors of 201 Solved Examples

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

Example 1

How many factors of 201 are there?

Solution

The total number of Factors of 201 is 4.

Factors of 201 are 1, 3, 67, and 201.

Example 2

Find the factors of 201 using prime factorization.

Solution

The prime factorization of 201 is given as:

201 $\div$ 3 = 67

67 $\div$ 67 = 1 

So the prime factorization of 201 can be written as:

3 x 67 = 201

Factors of 200|Factors List| Factors of 202