Factors of 270: Prime Factorization, Methods, and Examples

The factors of 270 are the integers that are entirely divisible by 270. It has 16 factors in total. This indicates that 16 factors are positive and 16 are negative. Negative factors of 270 are exactly similar to positive with a negative sign. 

Factors Of 270

The factors of 270 can be found using the division method and prime factorization.

Factors of 270

Here are the factors of number 270.

Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270

Negative Factors of 270

The negative factors of 270 are similar to its positive aspects, just with a negative sign.

Negative Factors of X: –1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -90, -135, and -270

Prime Factorization of 270

The prime factorization of 270 is the way of expressing its prime factors in the product form.

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

In this article, we will learn about the factors of 270 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 270?

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270. These numbers are the factors as they do not leave any remainder when divided by 270.

The factors of 270 are classified as prime numbers and composite numbers. The prime factors of the number X can be determined using the prime factorization technique.

How To Find the Factors of 270?

You can find the factors of 270 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 270, create a list containing the numbers that are exactly divisible by X with zero remainders. One important thing to note is that 1 and 270 are the 270’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 270 are determined as follows:

\[\dfrac{270}{1} = 270\]

\[\dfrac{270}{2} = 135\]

\[\dfrac{270}{3} = 90\]

\[\dfrac{270}{5} = 54\]

\[\dfrac{270}{6} = 45\]

\[\dfrac{270}{9} = 30\]

\[\dfrac{270}{10} = 27\]

\[\dfrac{270}{15} = 18\]

\[\dfrac{270}{270} = 1\]

Therefore, 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270. are the factors of X.

Total Number of Factors of 270

For 270, there are sixteen positive factors and sixteen negative ones. So in total, there are thirty-two factors of 270. 

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 X is given as:

Factorization of 270 is 1 x 2 x 3$^3$ x 5.

The exponent of 1, 2, and 5 is 1. The coefficient of 3 is 3.

Adding 1 to each and multiplying them together results in 32.

Therefore, the total number of factors of 270 is 32. 16 are positive, and 16 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 270 by Prime FactorizationFactor of 270 by Prime Factorization

The number 270 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.

Before finding the factors of 270 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 270, 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 270 can be expressed as:

270 = 2 x 3 x 3 x 3 x 5

Factors of 270 in PairsFactor of 270 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 270, the factor pairs can be found as:

1 x 270 = 270

2 x 135 = 270

3 x 90 = 270

5 x 54 = 270

6 x 45 = 270

9 x 30 = 270

10 x 27 = 270

15 x 18 = 270

The possible factor pairs of 270 are given as (1, 270), (2, 135), (3, 90), (5, 54), (6, 45), (9, 30), (10, 27), and (15, 18 ).

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

The negative factor pairs of X are given as:

-1 x -270 = 270

-2 x -135 = 270

-3 x -90 = 270

-5 x -54 = 270

-6 x -45 = 270

-9 x -30 = 270

-10 x -27 = 270

-15 x -18 = 270

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, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -90, -135, and -270 are called negative factors of 270.

Factors of 270 Solved Examples

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

Example 1

How many factors of 270 are there?

Solution

The total number of Factors of 270 is 16.

Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270. 

Example 2

Find the factors of 270 using prime factorization.

Solution

The prime factorization of 270 is given as:

270 $\div$ 2 = 135 

135 $\div$ 3 = 45

45 $\div$ 3 = 15

15 $\div$ 3 = 5 

5 $\div$ 5 = 1

So the prime factorization of 270 can be written as:

2 x 3 x 3 x 3 x 5 = 270

Factors of 269|Factors List| Factors of 271