Factors of 369: Prime Factorization, Methods, and Examples

The factors of 369 are the numbers that result into a zero remainder and a whole number quotient when they act as the divisors for the number 369. 

The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 369

Here are the factors of number 369.

Factors of 369: 1, 3, 9, 41, 123, 369

Negative Factors of 369

The negative factors of 369 are similar to its positive aspects, just with a negative sign.

Negative Factors of 369: -1, -3, -9, -41, -123, and -369

Prime Factorization of 369

The prime factorization of 369 is the way of expressing its prime factors in the product form.

Prime Factorization: $3^{2}$ x 41

In this article, we will learn about the factors of 369 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 369?

The factors of 369 are 1, 3, 9, 41, 123, and 369. These numbers are the factors as they do not leave any remainder when divided by 369.

The factors of 369 are classified as prime numbers and composite numbers. The prime factors of the number 369 can be determined using the prime factorization technique.

How To Find the Factors of 369?

You can find the factors of 369 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 369, create a list containing the numbers that are exactly divisible by 369 with zero remainders. One important thing to note is that 1 and 369 are the 369’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 369 are determined as follows:

\[\dfrac{369}{1} = 369\]

\[\dfrac{369}{3} = 123\]

\[\dfrac{369}{9} = 41\]

\[\dfrac{369}{369} = 1\]

Therefore, 1, 3, 9, and 369 along with their quotients 41 and 123 are the factors of 369.

Total Number of Factors of 369

For 369, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 369. 

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 369 is given as:

Factorization of 369 is 1 x $3^{2}$ x 41.

The exponent of 1 and 41 is 1 and 3 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 369 is 12. 6 are positive, and 6 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 369 by Prime Factorization

The number 369 is a composite 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 369 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 369, 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 369 can be expressed as:

369 = $3^{2}$ x 41

Factors of 369 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 369, the factor pairs can be found as:

1 x 369 = 369

3 x 123 = 369

9 x 41 = 369 

The possible factor pairs of 369 are given as (1, 369), (3, 123), and (9, 41).

All these numbers in pairs, when multiplied, give 369 as the product.

The negative factor pairs of 369 are given as:

-1 x -369 = 369

-3 x -123 = 369

-9 x -41 = 369 

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, -9, -41, -123, and -369 are called negative factors of 369.

The list of all the factors of 369, including positive as well as negative numbers, is given below.

Factor list of 369: 1, -1, 3, -3, 9, -9, 41, -41, 123, -123, 369, and -369

Factors of 369 Solved Examples

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

Example 1

How many factors of 369 are there?

Solution

The total number of Factors of 369 is 6.

Factors of 369 are 1, 3, 9, 41, 123, and 369.

Example 2

Find the factors of 369 using prime factorization.

Solution

The prime factorization of 369 is given as:

369 $\div$ 3 = 123 

123 $\div$ 3 = 41

41 $\div$ 41 = 1 

So the prime factorization of 369 can be written as:

$3^{2}$ x 41 = 369

Factors of 368|Factors List| Factors of 370