Factors of 677: Prime Factorization, Methods, and Examples

In this article, we will prove that the number 677 has only two factors, which are 1 and the number 677 itself which means that there are only two numbers on the number line that completely divide 677, the remainder is zero. 

Factors Of 677

Other than these two all other numbers give a non-zero remainder on division.

Factors of 677

Here are the factors of number 677.

Factors of 677: 1 and 677

Negative Factors of 677

The negative factors of 677 are similar to its positive aspects, just with a negative sign.

Negative Factors of 677: -1 and -677

Prime Factorization of 677

The prime factorization of 677 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 677

In this article, we will learn about the factors of 677 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 677?

The factors of 677 are 1 and 677. These numbers are the factors as they do not leave any remainder when divided by 677.

The factors of 677 are classified as prime numbers and composite numbers. The prime factors of the number 677 can be determined using the prime factorization technique.

How To Find the Factors of 677?

You can find the factors of 677 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 677, create a list containing the numbers that are exactly divisible by 677 with zero remainders. One important thing to note is that 1 and 677 are the 677’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 677 are determined as follows:

\[\dfrac{677}{1} = 677\]

\[\dfrac{677}{677} = 1\]

Therefore, 1 and 677 are the factors of 677.

Total Number of Factors of 677

For 677, there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 677. 

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 677 is given as:

The factorization of 677 is 1 x 677.

The exponent of 1 and 677 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 677 is 4. 2 are positive, and 2 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 677 by Prime Factorization

The number 677 is a prime 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 677

Before finding the factors of 677 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 677, 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 67 can be expressed as:

677 = 1 x 677

Factors of 677 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 677 in Pairs

For 677, the factor pairs can be found as:

1 x 677 = 677

The possible factor pairs of 677 are given as (1, 677) .

All these numbers in pairs, when multiplied, give 677 as the product.

The negative factor pairs of 677 are given as:

-1 x -677 = 677 

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 and -677 are called negative factors of 677.

The list of all the factors of 677, including positive as well as negative numbers, is given below.

Factor list of 677: 1, -1, 677, and -677.

Factors of 677 Solved Examples

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

Example 1

How many factors of 677 are there?


The total number of Factors of 677 is 2.

Factors of 677 are 1 and 677

Example 2

Find the factors of 677 using prime factorization.


The prime factorization of 677 is given as:

677 $\div$ 677 = 1 

So the prime factorization of 677 can be written as:

1 x 677 = 677

Factors of 676|Factors List| Factors of 678