Factors of 546: Prime Factorization, Methods, and Examples

546 is an even number which makes the smallest and only even prime number, 2 its factor.  546 has factors other than 546 and the universal prime number i.e. 1 which makes 546 an even composite number.

The factors of a number are either equal or smaller than the number itself as the number is a multiple of its factors.

Factors of 546

Here are the factors of number 546.

Factors of 546: 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273 and 546

Negative Factors of 546

The negative factors of 546 are similar to its positive aspects, just with a negative sign.

Negative Factors of 546: -1, -2, -3, -6, -7, -13, -14, -21, -26, -39, -42, -78, -91, -182, -273 and -546

Prime Factorization of 546

The prime factorization of 546 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 7 x 13

In this article, we will learn about the factors of 546 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 546?

The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273 and 546. These numbers are the factors as they do not leave any remainder when divided by 546.

The factors of 546 are classified as prime numbers and composite numbers. The prime factors of the number 546 can be determined using the prime factorization technique.

How To Find the Factors of 546?

You can find the factors of 546 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 546, create a list containing the numbers that are exactly divisible by 546 with zero remainders. One important thing to note is that 1 and 546 are the 546’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 546 are determined as follows:

$\dfrac{546}{1} = 546$

$\dfrac{546}{2} = 273$

$\dfrac{546}{3} = 182$

$\dfrac{546}{6} = 91$

$\dfrac{546}{7} = 78$

$\dfrac{546}{13} = 42$

$\dfrac{546}{14} = 39$

$\dfrac{546}{21} = 26$

$\dfrac{546}{26} = 21$

$\dfrac{546}{39} = 14$

$\dfrac{546}{42} = 13$

$\dfrac{546}{78} = 7$

$\dfrac{546}{91} = 6$

$\dfrac{546}{182} = 3$

$\dfrac{546}{273} = 2$

$\dfrac{546}{546} = 1$

Therefore, 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273 and 546 are the factors of 546.

Total Number of Factors of 546

For 546, there are 16 positive factors and 16 negative ones. So in total, there are  factors of 546.

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 546 is 1 x 2 x 3 x 7 x 13.

The exponent of 1, 2, 3, 7, and 13 is 1.

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

Therefore, the total number of factors of 546 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 546 by Prime Factorization

The number 546 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.

Before finding the factors of 546 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 546, 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 546 can be expressed as:

546 = 2 x 3 x 7 x 13

Factors of 546 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 546, the factor pairs can be found as:

1 x 546 = 546

2 x 273 = 546

3 x 182 = 546

6 x 91 = 546

7 x 78 = 546

13 x 42 = 546

14 x 39 = 546

21 x 26 = 546

The possible factor pairs of 546 are given as (1, 546), (2, 273), (3, 182), (6, 91), (7, 78), (13, 42), (14, 39) and (21, 26).

All these numbers in pairs, when multiplied, give 546 as the product.

The negative factor pairs of 546 are given as:

-1 x -546 = 546

-2 x -273 = 546

-3 x -182 = 546

-6 x -91 = 546

-7 x -78 = 546

-13 x -42 = 546

-14 x -39 = 546

-21 x -26 = 546

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, -6, -7, -13, -14, -21, -26, -39, -42, -78,- 91, -182, -273 and -546 are called negative factors of 546.

The list of all the factors of 546, including positive as well as negative numbers, is given below.

Factor list of 546: 1, -1, 2, -2, 3, -3, 6, -6, 7, -7, 13, -13, 14, -14, 21, -21, 26, -26, 39, -39 42, -42, 78, -78, 91, -91, 182, -182, 273, -273, 546, and -546

Factors of 546 Solved Examples

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

Example 1

How many factors of 546 are there?

Solution

The total number of Factors of 546 is 16.

Factors of 546 are1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273 and 546

Example 2

Find the factors of 546 using prime factorization.

Solution

The prime factorization of 546 is given as:

546 $\div$ 2 = 273

273 $\div$ 3 = 91

91 $\div$ 7 = 13

13 $\div$ 13 = 1

So the prime factorization of 546 can be written as:

2 x 3 x 7 x 13 = 546