Factors of 320: Prime Factorization, Methods, and Examples

The factors of 320 are the list of numbers that divides 320 equally without a remainder. 320 is an even number. It is also a composite as it has more than two factors. 

Factors Of 320

Let us find out more about the factors of 320.

Factors of 320

Here are the factors of number 320.

Factors of 320: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, and 320

Negative Factors of 320

The negative factors of 320 are similar to its positive aspects, just with a negative sign.

Negative Factors of 320: – 1, -2, -4, -5, -8, -10, -16, -20, -32, -40, -64, -80, -160, and -320

Prime Factorization of 320

The prime factorization of 320 is the way of expressing its prime factors in the product form.

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

In this article, we will learn about the factors of 320 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 320?

The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, and 320. These numbers are the factors as they do not leave any remainder when divided by 320.

The factors of 320 are classified as prime numbers and composite numbers. The prime factors of the number 320 can be determined using the prime factorization technique.

How To Find the Factors of 320?

You can find the factors of 320 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 320, create a list containing the numbers that are exactly divisible by 320 with zero remainders. One important thing to note is that 1 and 320 are 320’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 320 are determined as follows:

\[\dfrac{320}{1} = 320\]

\[\dfrac{320}{2} = 160\]

\[\dfrac{320}{4} = 80\]

\[\dfrac{320}{5} = 64\]

\[\dfrac{320}{8} = 40\]

\[\dfrac{320}{10} = 32\]

\[\dfrac{320}{16} = 20\]

\[\dfrac{320}{320} = 1\]

Therefore, 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, and 320 are the factors of 320.

Total Number of Factors of 320

For 320, there are fourteen positive factors and fourteen negative ones. So in total, there are twenty-eight factors of 320. 

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 320 is given as:

Factorization of 320 is 1 x 2$^6$ x 5.

The exponent of 1 and 5 is 1. The exponent of 2 is 6.

Adding 1 to each and multiplying them together results in 28.

Therefore, the total number of factors of 320 is 28. Fourteen factors are positive, and fourteen 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 320 by Prime Factorization

The number 320 is a composite. 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 320

Before finding the factors of 320 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 320, 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 320 can be expressed as:

320 = 2$^6$ x 5

Factors of 320 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 320 in Pairs

For 320, the factor pairs can be found as:

1 x 320 = 320

2 x 160 = 320 

4 x 80 = 320

5 x 64 = 320

8 x 40 = 320

10 x 32 = 320

16 x 20 = 320

The possible factor pairs of 320 are given as (1, 320), (2, 160), (4, 80), (5, 64), (8, 40), (10, 32), and (16, 20 ).

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

The negative factor pairs of 320 are given as:

-1 x -320 = 320

-2 x -160 = 320 

-4 x -80 = 320

-5 x -64 = 320

-8 x -40 = 320

-10 x -32 = 320

-16 x -20 = 320

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, -4, -5, -8, -10, -16, -20, -32, -40, -64, -80, -160, and -320 are called negative factors of 320.

Factors of 320 Solved Examples

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

Example 1

How many factors of 320 are there?

Solution

The total number of Factors of 320 is fourteen.

Factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, and 320

Example 2

Find the factors of 320 using prime factorization.

Solution

The prime factorization of 320 is given as:

320 $\div$ 2 = 160 

160 $\div$ 2 = 80

80 $\div$ 2 = 40

40 $\div$ 2 = 20

20 $\div$ 2 = 10

10 $\div$ 2 = 5     

5 $\div$ 5 = 1 

So the prime factorization of 320 can be written as:

2$^6$ x 5 = 320

Factors of 319|Factors List| Factors of 321