banner

Factors of 167: Prime Factorization, Methods, and Examples

Factors of 167 are the numbers in pairs that, when multiplied together, result in 167. 167 is a prime number which means that it has only two factors.

The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 167

Here are the factors of number 167.

Factors of 167: 1, 167

Negative Factors of 167

The negative factors of 167 are similar to the positive ones, with a negative sign.

Negative Factors of 167: -1, -167

Prime Factorization of 167

The prime factorization of 167 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 167

In this article, we will learn about the factors of 167 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 167?

The factors of 167 are 1 and 167. All of these numbers are the factors as they do not leave any remainder when divided by 167.

The factors of 167 are 1 and 167, as 167 is a prime number. The prime factors of the number 167 can be determined using the prime factorization technique.

How To Find the Factors of 167?

You can find the factors of 167 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 167, create a list containing the numbers precisely divisible by 167 with zero remainders. One important thing to note is that 1 and 167 are the 167’s factors as every natural number has one and the number itself as its factor.

One is also called the universal factor of every number. The factors of 167 are determined as follows:

\[\dfrac{167}{1} = 167\]

Therefore, 1 and 167 are the factors of 167.

Total Number of Factors of 167

For 167, there are two positive factors and two negative ones. So in total, there are four factors of 167. 

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 167 is given as:

The factorization of 167 is 1 x 167.

The exponent of 1 and 167 is 1.

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

Therefore, the total number of factors of 167 is 4. 2 are positive, and two are negative.

Important Notes

Here are some important 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 167 by Prime Factorization

The number 167 is a prime number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 167 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 167, start dividing by its smallest 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 167 can be expressed as:

167 = 1 x 167

Factors of 167 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 of the given numbers.

167 is a prime number; therefore, it has only a one-factor pair.

1 x 167 = 167 

The possible factor pair of 167 is given as (1, 167).

The negative factor pair of 167 is given as:

 -1 x -167 = 167 

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 -167 are called negative factors of 167.

The list of all the factors of 167, including positive and negative numbers, is given below.

Factor list of 167: 1, -1, 167, and -167

Factors of 167 Solved Examples

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

Example 1

How many factors of 167 are there?

Solution

The total number of Factors of 167 is 2.

Factors of 167 are 1 and 167.

Example 2

Find the factors of 167 using prime factorization.

Solution

The prime factorization of 167 is given as:

167 $\div$ 1 = 167

So the prime factorization of 167 can be written as:

1 x 167 = 167 

Factors of 166| Factors List| Factors of 168

5/5 - (5 votes)