Factors of 202: Prime Factorization, Methods, and Examples

The factors of 202 are the numbers that give zero as a remainder. When they act as the divisors, these factors also yield a whole number quotient. The number 202 is an even composite number, so it has 2 in its factor list. 

Factors Of 202

The factors of 202 are both positive and negative. 

Factors of 202

Here are the factors of number 202.

Factors of 202: 1, 2, 101, 202

Negative Factors of 202

The negative factors of 202 are similar to its positive factors, just with a negative sign.

Negative Factors of 202: -1, -2, -101, and -202

Prime Factorization of 202

The prime factorization of 202 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 101

In this article, we will learn about the factors of 202 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 202?

The factors of 202 are 1, 2, 101, and 202. All of these numbers are the factors as they do not leave any remainder when divided by 202.

The factors of 202 are classified as prime numbers and composite numbers. The prime factors of the number 202 can be determined using the prime factorization technique.

How To Find the Factors of 202?

You can find the factors of 202 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 202, create a list containing the numbers that are exactly divisible by 202 with zero remainders. One important thing to note is that 1 and 202 are 202’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 202 are determined as follows:

\[\dfrac{202}{1} = 202\]

\[\dfrac{202}{2} = 101\]

\[\dfrac{202}{101} = 2\]

\[\dfrac{202}{202} = 1\]

Therefore, 1, 2, 101, and 202 are the factors of 202.

Total Number of Factors of 202

For 202, there are four positive factors and four negative ones. So in total, there are eight factors of 202. 

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 202 is given as:

Factorization of 202 is 1 x 2 x 101.

The exponent of all factors is 1.

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

Therefore, the total number of factors of 202 is 8. 4 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 202 by Prime FactorizationFactor of 202 by Prime Factorization

The number 202 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 202 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 202, 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 202 can be expressed as:

202 = 2 x 101

Factors of 202 in PairsFactor of 202 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.

For 202, the factor pairs can be found as:

1 x 202 = 202

2 x 101 = 202

The possible factor pairs of 202 are given as (1, 202) and (2, 101).

All these numbers in pairs, when multiplied, give 202 as the product.

The negative factor pairs of 202 are given as:

-1 x -202= 202

 -2 x -101 = 202

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, -2, -101, and -202 are negative factors of 202.

The list of all the factors of 202, including positive as well as negative numbers, is given below.

Factor list of 202: 1, -1, 2, -2, 101, -101, 202, and -202

Factors of 202 Solved Examples

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

Example 1

How many factors of 202 are there?

Solution

The total number of Factors of 202 is 4.

Factors of 202 are 1, 2, 101, and 202.

Example 2

Find the factors of 202 using prime factorization.

Solution

The prime factorization of 202 is given as:

202 $\div$ 2 = 101 

101 $\div$ 101 = 1 

So the prime factorization of 202 can be written as:

 2 x 101 = 202 

Factors of 201|Factors List| Factors of 203