banner

Factors of 678: Prime Factorization, Methods, and Examples

678 is an even composite number and the fact will be explained in detail in this article. This article will teach you to find the factors of 678 by different methods. 

The number 678 has 8 factors in total and the list includes 1, 2, 3, 6, 113, 226, 339, and 678.

Factors of 678

Here are the factors of number 678.

Factors of 678: 1, 2, 3, 6, 113, 226, 339, and 678.

Negative Factors of 678

The negative factors of 678 are similar to its positive aspects, just with a negative sign.

Negative Factors of 678: -1, -2, -3, -6, -113, -226, -339, and -678.

Prime Factorization of 678

The prime factorization of 678 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 113

In this article, we will learn about the factors of 678 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 678?

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, and 678. These numbers are the factors as they do not leave any remainder when divided by 678.

The factors of 678 are classified as prime numbers and composite numbers. The prime factors of the number 678 can be determined using the prime factorization technique.

How To Find the Factors of 678?

You can find the factors of 678 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 678, create a list containing the numbers that are exactly divisible by 678 with zero remainders. One important thing to note is that 1 and 678 are the X’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 578 are determined as follows:

\[\dfrac{678}{1} = 678\]

\[\dfrac{678}{2} = 339\]

\[\dfrac{678}{3} = 226\]

\[\dfrac{678}{6} = 113\]

\[\dfrac{678}{113} = 6\]

\[\dfrac{678}{226} = 3\]

\[\dfrac{678}{339} = 2\]

\[\dfrac{678}{678} = 1\]

Therefore, 1, 2, 3, 6, 113, 226, 339, and 678 are the factors of 678.

Total Number of Factors of 678

For 678, there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 678. 

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 678 is given as:

Factorization of 678 is 1 x 2 x 3 x 113.

The exponent of 1, 2, 3, and 113 is 1.

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

Therefore, the total number of factors of 678 is 16. 8 are positive, and 8 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 678 by Prime Factorization

The number 678 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 678 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 678, 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 678 can be expressed as:

678 = 2 x 3 x 113

Factors of 678 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 678, the factor pairs can be found as:

1 x 678 = 678

2 x 339 = 678 

3 x 226 = 678 

6 x 113 = 678 

The possible factor pairs of 678 are given as (1, 678), (2, 399), (3, 226), and (6, 113 ).

All these numbers in pairs, when multiplied, give 678 as the product.

The negative factor pairs of 678 are given as:

-1 x -678 = 678

-2 x -339 = 678 

-3 x -226 = 678 

-6 x -113 = 678 

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, -113, -226, -339, and -678. are called negative factors of 678.

The list of all the factors of 678, including positive as well as negative numbers, is given below.

Factor list of 678: 1, -1, 2, -2, 3, -3, 6, -6, 113, -113, 226, -226, 339, -339, 678, and -678.

Factors of 678 Solved Examples

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

Example 1

How many factors of 678 are there?

Solution

The total number of Factors of 678 is 16.

Factors of 678 are 1, 2, 3, 6, 113, 226, 339, and 678.

Example 2

Find the factors of 678 using prime factorization.

Solution

The prime factorization of 678 is given as:

678 $\div$ 2 = 339 

339 $\div$ 3 = 113 

113 $\div$ 113 = 1 

So the prime factorization of 678 can be written as:

2 x 3 x 113 = 678

Factors of 677|Factors List| Factors of 679

5/5 - (5 votes)