Factors of 361: Prime Factorization, Methods, and Examples

The numbers on which 361 is divisible, that is, on which 361may be divided without leaving any remainder, are known as its factors.

Factors Of 361

Factors of 361

Here are the factors of number 361.

Factors of 361: 1, 19 and 361

Negative Factors of 361

The negative factors of 361 are similar to their positive aspects, just with a negative sign.

Negative Factors of 361: -1, -19  and -361

Prime Factorization of 361

The prime factorization of 361 is the way of expressing its prime factors in the product form.

Prime Factorization: 192

In this article, we will learn about the factors of 361 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 361?

The factors of 361 are 1, 19, and 361. These numbers are the factors as they do not leave any remainder when divided by 361.

The factors of 361 are classified as prime numbers and composite numbers. The prime factors of the number 361 can be determined using the prime factorization technique.

How To Find the Factors of 361?

You can find the factors of 361 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 361, create a list containing the numbers that are exactly divisible by 361 with zero remainders. One important thing to note is that 1 and 361 are the361’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 361 are determined as follows:

\[\dfrac{361}{1} = 361\]

\[\dfrac{361}{19} = 19\]

\[\dfrac{19}{19} = 1\]

Therefore,1, 19, and 361 are the factors of 361.

Total Number of Factors of 361

For 361, there are 3 positive factors and 3 negative ones. So in total, there are 6 factors of 361. 

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 361 is given as:

Factorization of 361 is 1, 19, and 361.

The exponent of a, b, and c is 1.

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

Therefore, the total number of factors of 361 is 6. 3 is positive, and 33 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 361 by Prime Factorization

The number 361 is a composite/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.prime factorization of 361

Before finding the factors of 361 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 361, 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 361 can be expressed as:

361 = 192

Factors of 361 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.Factors of 361 in Pairs

For 361, the factor pairs can be found as:

1 x 361 = 361

19 x 19 = 361 

The possible factor pairs of 361 are given as (1, 361) and (19, 19 ).

All these numbers in pairs, when multiplied, give 361 as the product.

The negative factor pairs of 361 are given as:

-1 x -361 = 361

-19 x -19 = 361 

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, -19, and -361 are called negative factors of 361.

The list of all the factors of 361, including positive as well as negative numbers, is given below.

Factor list of 361: 1,-1, 19,-19 , 361, and -361

Factors of 361 Solved Examples

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

Example 1

How many factors of 361 are there?


The total number of Factors of 361 is 6.

Factors of 361 are 1, 19, and 361.

Example 2

Find the factors of 361 using prime factorization.


The prime factorization of 361 is given as:

361 $\div$ 19 = 19 

19 $\div$ 19 = 1 

So the prime factorization of 361 can be written as:

192 = 361

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