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Factors of 188: Prime Factorization, Methods, and Examples

The factors of 188 are numbers that make 188 completely divisible upon them. These numbers give a whole number quotient and zero as the remainder.

These factors can be determined using the method of prime factorization.  The number 188 has both positive and negative factors.

Factors of 188

Here are the factors of number 188.

Factors of X: 1, 2, 4, 47, 94, 188

Negative Factors of 188

The negative factors of 188 are similar to its positive factors, just with a negative sign.

Negative Factors of X: -1, -2, -4, -47,-94 and -188

Prime Factorization of 188

The prime factorization of 188 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 47

In this article, we will learn about the factors of 188 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 188?

The factors of 188 are 1, 2, 4, 47, 94, and 188. All of these numbers are the factors as they do not leave any remainder when divided by 188.

The factors of 188 are classified as prime numbers and composite numbers. The prime factors of the number 188 can be determined using the technique of prime factorization.

How To Find the Factors of 188?

You can find the factors of 188 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 188, create a list containing the numbers that are exactly divisible by 188 with zero remainders. One important thing to note is that 1 and 188 are the 188’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 188 are determined as follows:

\[\dfrac{188}{1} = 188\]

\[\dfrac{188}{2} = 94\]

\[\dfrac{188}{4} = 47\]

\[\dfrac{188}{188} = 1\]

Therefore, 1, 2, 4, 47, 94, and 188 are the factors of 188.

Total Number of Factors of 188

For 188 there are 6 positive factors and 6 negative ones. So in total, there are m factors of 12. 

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 188 is given as:

Factorization of X is 1 x 2^{2} x 47.

The exponent of 1, and 47 is 1. Whereas the exponent of 2 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 188 is 12. 6 are positive and 6 factors 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 188 by Prime Factorization

The number 188 is a composite 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 188 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 188, 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 188 can be expressed as:

\[  188 = 2 \times 2 \times 47\]

Factors of X 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.

For X, the factor pairs can be found as:

\[ 1 \times 188 = 188 \]

\[ 2 \times 94 = 188 \]

\[ 4 \times 47 = 188 \]

The possible factor pairs of 188 are given as (1, 188),(2, 94 ), and(4, 37 ).

All these numbers in pairs, when multiplied, give 188 as the product.

The negative factor pairs of 188 are given as:

\[ -1 \times -188 = 188 \]

\[ -2 \times -94 = 188 \]

\[ -4 \times -47 = 188 \]

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, -4, -47,-94 and -188 are called negative factors of 188.

The list of all the factors of 188 including positive as well as negative numbers is given below.

Factor list of 188: 1, -1, 2, -2, 4, -4, 47, -47, -94, 94, 188, and -188

Factors of 188 Solved Examples

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

Example 1

How many factors of 188 are there?

Solution

The total number of Factors of 188 is 6.

Factors of 188 are 1, 2, 4, 47, 94, and 188.

Example 2

Find the factors of 188 using prime factorization.

Solution

The prime factorization of 188 is given as:

\[ 188 \div 2 = 94 \]

\[ 94 \div 2 = 47 \]

\[ 47 \div 47 = 1 \]

So the prime factorization of X can be written as:

\[ 2^{2} \times 47 = 188 \]

Factors of 187|Factors List| Factors of 189

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