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Factors of 377: Prime Factorization, Methods, and Examples

The prime factor of number 377 is those factor numbers when multiply those factors give back the same number 377. Factors of 377 are elaborate in detail with an example below in this article but shortly if we discuss factors 377 are 1,13, 29, and 377 are the factors. 

The number 377 is an odd number and it is composite too because it has more than two factors.

Factors of 377

Here are the factors of number 377.

Factors of 377: 1, 13, 29, and 377

Negative Factors of 377

The negative factors of 377 are similar to their positive aspects, just with a negative sign.

Negative Factors of 377: -1, -13, -29, and -377

Prime Factorization of 377

The prime factorization of 377 is the way of expressing its prime factors in the product form.

Prime Factorization:  13 x 29

In this article, we will learn about the factors of 377 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 377?

The factors of 377 are 1, 13, 29, and 377. These numbers are the factors as they do not leave any remainder when divided by 377.

The factors of 377 are classified as prime numbers and composite numbers. The prime factors of the number 377 can be determined using the prime factorization technique.

How To Find the Factors of 377?

You can find the factors of 377 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 377, create a list containing the numbers that are exactly divisible by 377 with zero remainders. One important thing to note is that 1 and 377 are the 377’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 348 are determined as follows:

\[\dfrac{377}{1} = 377\]

\[\dfrac{377}{13} = 29\]

\[\dfrac{377}{29} = 13\]

\[\dfrac{377}{377} = 1\]

Therefore, 1, 13, 29, and 377 are the factors of 377.

Total Number of Factors of 377

For 377, there are four positive factors and four negative ones. So in total, there are eight factors of 377.

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 377 is given as:

Factorization of 377 is 1 x 13 x 29.

The exponent of 1 x 13 x 29 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 377 is 8. Four are positive, and 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 377 by Prime Factorization

The number 377 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 377 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 377, 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 377 can be expressed as:

377 =  13 x 29

Factors of 377 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 377, the factor pairs can be found as:

1 x 377 = 377

13 x 29 = 377 

The possible factor pairs of 348 are given as (1, 377), and (13, 29).

All these numbers in pairs, when multiplied, give 377 as the product.

The negative factor pairs of 377 are given as:

-1 x -377 = 377

-13 x -29 = 377

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, -13, -29, and -377 are called negative factors of 377.

The list of all the factors of 377, including positive as well as negative numbers, is given below.

Factor list of 377: 1, -1, 13, -13, 29, -29, 377 and -377

Factors of 377 Solved Examples

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

Example 1

How many factors of 377 are there?

Solution

The total number of Factors of 377 is four.

Factors of 377 are 1, 13, 29, and 377.

Example 2

Find the factors of 377 using prime factorization.

Solution

The prime factorization of 377 is given as:

377 $\div$ 13 = 29 

29 $\div$ 29 = 1

So the prime factorization of 377 can be written as:

13 x 29 = 377

Factors of 376|Factors List| Factors of 378

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