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Factors of 660: Prime Factorization, Methods, and Examples

The factors of 660  are the group of numbers that can be divided by 660 without any remainder. The number 660 is a composite number with 24 factors in total. The biggest factors of 660 are 660 itself. 

Let us find out the factors of 660 and understand the concept better.

Factors of 660

Here are the factors of number 660.

Factors of 660: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, and 660 

Negative Factors of 660

The negative factors of 660 are similar to their positive aspects, just with a negative sign.

Negative Factors of 660: –1, -2, -3, -4, -5, -6, -10, -11, -12, -15, -20, -22, -30, -33, -44, -55, -60, -66, -110, -132, -165, -220, -330, and -660 

Prime Factorization of 660

The prime factorization of 660 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 3 x 5 x 11

In this article, we will learn about the factors of 660 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 660?

The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, and 660. These numbers are the factors as they do not leave any remainder when divided by 660.

The factors of 660 are classified as prime numbers and composite numbers. The prime factors of the number 660 can be determined using the prime factorization technique.

How To Find the Factors of 660?

You can find the factors of 660 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 660, create a list containing the numbers that are exactly divisible by 660 with zero remainders. One important thing to note is that 1 and 660 are 660’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 660 are determined as follows:

\[\dfrac{660}{1} = 660\]

\[\dfrac{660}{2} = 330\]

\[\dfrac{660}{3} = 220\]

\[\dfrac{660}{4} = 165\]

\[\dfrac{660}{5} = 132\]

\[\dfrac{660}{6} = 110\]

\[\dfrac{660}{10} = 66\]

\[\dfrac{660}{11} = 60\]

\[\dfrac{660}{12} = 55\]

\[\dfrac{660}{15} = 44\]

\[\dfrac{660}{20} = 33\]

\[\dfrac{660}{22} = 30\]

Therefore, 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, and 660 are the factors of 660.

Total Number of Factors of 660

For 660, there are twenty-four positive factors and twenty-four negative ones. So in total, there are forty-eight factors of 660. 

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 660 is given as:

Factorization of 660 is 1 x 2$^2$ x 5 x 11.

The exponent of 1, 5, and 11 is 1. The exponent of 2 is 2.

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

Therefore, the total number of factors of 660 is 48. Twenty-four are positive, and twenty-four 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 660 by Prime Factorization

The number 660 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 660 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 660, 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 660 can be expressed as:

660 = 2 x 2 x 3 x 5 x 11

Factors of 660 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 660, the factor pairs can be found as:

1 x 660 = 660

2 x 330 = 660

3 x 220 = 660

4 x 165 = 660

5 x 132 = 660

6 x 110 = 660

10 x 66 = 660

11 x 60 = 660

12 x 55 = 660

15 x 44 = 660

20 x 33 = 660

         22 x 30 = 660         

The possible factor pairs of 660 are given as (1, 660), (2, 330), (3, 220), (4, 165), (5, 132), (6, 110), (10, 66), (11, 60), (12, 55), (15, 44), (20, 33), and (22, 30).

All these numbers in pairs, when multiplied, give 660 as the product.

The negative factor pairs of 660 are given as:

-1 x -660 = 660

-2 x -330 = 660

-3 x -220 = 660

-4 x -165 = 660

-5 x -132 = 660

-6 x -110 = 660

-10 x -66 = 660

-11 x -60 = 660

-12 x -55 = 660

-15 x -44 = 660

-20 x -33 = 660

 -22 x -30 = 660

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, -4, -5, -6, -10, -11, -12, -15, -20, -22, -30, -33, -44, -55, -60, -66, -110, -132, -165, -220, -330, and -660 are called negative factors of 660.

The list of all the factors of 660, including positive as well as negative numbers, is given below.

Factor list of 660: 1, 1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 10, -10, 11, -11, 12, -12, 15, -15, 20, -20, 22, -22, 30, -30, 33, -33, 44, -44, 55, -55, 60, -60, 66, -66, 110, -110, 132, -132, 165, -165, 220, -220, 330, -330, 660, and -660 

Factors of 660 Solved Examples

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

Example 1

How many factors of 660 are there?

Solution

The total number of Factors of 660 is 24.

Factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, and 660.

Example 2

Find the factors of 660 using prime factorization.

Solution

The prime factorization of 660 is given as:

660 $\div$ 2 = 330 

330 $\div$ 2 = 165

165 $\div$ 5 = 33

33 $\div$ 3 = 11   

11 $\div$ 11 = 1 

So the prime factorization of 660 can be written as:

2 x 2 x 3 x 5 x 11 = 660

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