Factors of 360: Prime Factorization, Methods, and Examples

When subtracted from 360, the numbers that leave zero as the remainder are known as the factors of 360. 

These figures also fail to account for the whole number quotient.

Factors of 360

Here are the factors of number 360.

Factors of 360: 1, 2, 180, 360

Negative Factors of 360

The negative factors of 360 are similar to its positive aspects, just with a negative sign.

Negative Factors of 360: -1, -2, -180, and -360

Prime Factorization of 360

The prime factorization of 360 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 3 x 3 x 5

In this article, we will learn about the factors of 360 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 360?

The factors of 360 are 1, 2, 180, and 360. These numbers are the factors as they do not leave any remainder when divided by 360.

The factors of 360 are classified as prime numbers and composite numbers. The prime factors of the number 360 can be determined using the prime factorization technique.

How To Find the Factors of 360?

You can find the factors of 360 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 360, create a list containing the numbers that are exactly divisible by 360 with zero remainders. One important thing to note is that 1 and 360 are the 360’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 360 are determined as follows:

\[\dfrac{360}{1} = 360\]

\[\dfrac{360}{2} = 180\]

\[\dfrac{360}{180} = 2\]

\[\dfrac{360}{360} = 1\]

Therefore, 1, 2, 180, and 360 are the factors of 360.

Total Number of Factors of 360

For 360, there are 24 positive factors and 24 negative ones. So in total, there are 48 factors of 360. 

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. Then, 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 360 is given as:

Factorization of 360 is 1 x 2 x 180.

The exponent of 1, 2, and 180 is 1.

Adding 1 to each and multiplying them together results in 48.

Therefore, the total number of factors of 360 is 48. 24 are positive, and 24 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 number factors 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 360 by Prime Factorization

The number 360 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.

Before finding the factors of 360 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 360, 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 360 can be expressed as:

360 = 2 x 180

Factors of 360 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 360, the factor pairs can be found as:

1 x 360 = 360

2 x 180 = 360

The possible factor pairs of 360 are given as (1, 360) and (2, 180 ).

All these numbers in pairs, when multiplied, give 360 as the product.

The negative factor pairs of 360are given as:

-1 x -360 = 360

-2 x -180 = 360

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, -180, and -360 are called negative factors of 360.

The list of all the factors of 360, including positive as well as negative numbers, is given below.

Factor list of 360: 1, -1, 2, -2, 180, -180, 360, and -360

Factors of 360 Solved Examples

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

Example 1

How many factors of 360 are there?

Solution

The total number of Factors of 360 is 48.

Factors of 360 are 1, 2, 180, and 360.

Example 2

Find the factors of 360 using prime factorization.

Solution

The prime factorization of 360 is given as:

360 $\div$ 2 = 180 

180 $\div$ 180 = 1 

So the prime factorization of 360 can be written as:

2 x 180 = 360

Factors of 359|Factors List| Factors of 361