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Factors of 648: Prime Factorization, Methods, and Examples

The number 648 given in this article is an even composite number. It has a total of 40 factors out of which 20 are positive and 20 are negative. Factors are the numbers that when divided by the original number, leave a 0 remainder

Factors Of 648

This is the information provided in the article in detail.

Factors of 648

Here are the factors of number 648.

Factors of 648: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648

Negative Factors of 648

The negative factors of 648 are similar to its positive aspects, just with a negative sign.

Negative Factors of 648: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -324, and -648

Prime Factorization of 648

The prime factorization of 648 is the way of expressing its prime factors in the product form.

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

In this article, we will learn about the factors of 648 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 648?

The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648. These numbers are the factors as they do not leave any remainder when divided by 648.

The factors of 648 are classified as prime numbers and composite numbers. The prime factors of the number 648 can be determined using the prime factorization technique.

How To Find the Factors of 648?

You can find the factors of 648 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 648, create a list containing the numbers that are exactly divisible by 648 with zero remainders. One important thing to note is that 1 and 648 are the 648’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 648 are determined as follows:

\[\dfrac{648}{1} = 648\]

\[\dfrac{648}{2} = 324\]

\[\dfrac{648}{3} = 216\]

\[\dfrac{648}{4} = 162\]

\[\dfrac{648}{6} = 108\]

\[\dfrac{648}{8} = 81\]

\[\dfrac{648}{9} = 72\]

\[\dfrac{648}{12} = 54\]

\[\dfrac{648}{18} = 36\]

\[\dfrac{648}{24} = 27\]

\[\dfrac{648}{648} = 1\]

Therefore, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648 are the factors of 648.

Total Number of Factors of 648

For 648, there are 20 positive factors and 20 negative ones. So in total, there are 40 factors of 648. 

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 648 is given as:

Factorization of 648 is 1 x 2 x 2 x 2 x 3 x 3 x 3 x 3.

The exponent of 1, 2, and 3 is 1, 3, and 4 respectively.

Adding 1 to each and multiplying them together results in 40.

Therefore, the total number of factors of 648 is 40. 20 is positive, and 20 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 648 by Prime Factorization

The number 648 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.prime factorization of 648

Before finding the factors of 648 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 648, 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 648 can be expressed as:

648 = 2 x 2 x 2 x 3 x 3 x 3 x 3

Factors of 648 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 648 in Pairs

For 648, the factor pairs can be found as:

1 x 648 = 648

2 x 324 = 648

3 x 216 = 648

4 x 162 = 648

6 x 108 = 648

8 x 81 = 648

9 x 72 = 648

12 x 54 = 648

18 x 36 = 648

24 x 27 = 648

The possible factor pairs of 648 are given as (1, 648), (2 , 324), (3, 216), (4, 162), (6, 108), (8, 81), (9, 72), (12, 54), (18, 26), and (24, 27).

All these numbers in pairs, when multiplied, give 648 as the product.

The negative factor pairs of 648 are given as:

-1 x -648 = 648

-2 x -324 = 648

-3 x -216 = 648

-4 x -162 = 648

-6 x -108 = 648

-8 x -81 = 648

-9 x -72 = 648

-12 x -54 = 648

-18 x -36 = 648

-24 x -27 = 648

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, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -324, and -648 are called negative factors of 648.

The list of all the factors of 648, including positive as well as negative numbers, is given below.

Factor list of 648: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 18, -18, 24, -24, 27, -27, 36, -36, 54, -54, 72, -72, 81, -81, 108, -108, 162. -162, 216, -216, 324, -324, 648, and -648

Factors of 648 Solved Examples

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

Example 1

How many factors of 648 are there?

Solution

The total number of Factors of 648 is 40.

Factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648.

Example 2

Find the factors of 648 using prime factorization.

Solution

The prime factorization of 648 is given as:

648 $\div$ 2 = 324 

324 $\div$ 2 = 162

162 $\div$ 2 = 81

81 $\div$ 3 = 27

27 $\div$ 3 = 9

9 $\div$ 3 = 3

3 $\div$ 3 = 1 

So the prime factorization of 648 can be written as:

2 x 2 x 2 x 3 x 3 x 3 x 3 = 648

Factors of 647|Factors List| Factors of 649

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