Factors of 277: Prime Factorization, Methods, and Examples

The number 277 is a prime number that indicates that it has only two factors. Prime numbers are the numbers that can be divided by 1 and the number itself.

Factors Of 277

 277 has two factors that are divisible by 277, i.e., 1 and 277.

Factors of 277

Here are the factors of number 277.

Factors of 277: 1 and 277

Negative Factors of 277

The negative factors of 277 are similar to its positive aspects, just with a negative sign.

Negative Factors of 277: -1 and -277

Prime Factorization of 277

The prime factorization of 277 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 277

In this article, we will learn about the factors of 277 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 277?

The factors of 277 are 1 and 277. These numbers are the factors as they do not leave any remainder when divided by 277.

The factors of 277 are classified as prime numbers and composite numbers. The prime factors of the number 277 can be determined using the prime factorization technique.

How To Find the Factors of 277?

You can find the factors of 277 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 277, create a list containing the numbers that are exactly divisible by 277 and zero remainders. One important thing to note is that 1 and 277 are the 277’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 277 are determined as follows:

\[\dfrac{277}{1} = 277\]

Therefore, 1 and 277 are the factors of 277.

Total Number of Factors of 277

For 277, there are two positive factors and two negative ones. So in total, there are four factors of 277. 

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 277 is 1 x 277

The exponent of 1 and 277 is 1.

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

Therefore, the total number of factors of 277 is four. Two are positive, and two 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 277 by Prime FactorizationFactor of 277 by Prime Factorization

The number 277 is a composite/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.

Before finding the factors of 277 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 277, 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 277 can be expressed as:

277 = 1 x 277

Factors of 277 in PairsFactor of 277 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 277, the factor pairs can be found as:

1 x 277 = 277

The possible factor pair of 277 is given as (1, 277).

All these numbers in pairs, when multiplied, give 277 as the product.

The negative factor pair of 277 is given as:

-1 x -277 = 277 

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 -277 are called negative factors of 277.

The list of all the factors of 277, including positive as well as negative numbers, is given below.

Factor list of 277: 1, -1, 277, and -277

Factors of 277 Solved Examples

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

Example 1

How many factors of 277 are there?

Solution

The total number of Factors of 277 is two.

Factors of 277 are 1 and 277.

Example 2

Find the factors of 277 using prime factorization.

Solution

The prime factorization of 277 is given as:

277 $\div$ 1 = 277 

So the prime factorization of 277 can be written as:

1 x 277 = 277

Factors of 276|Factors List| Factors of 278