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Factors of 157: Prime Factorization, Methods, and Examples

The factors of 157 are the numbers upon which 157 is completely divisible. For these numbers, the divisors and their respective whole number quotient both act as the factors of 157.

Since the number 157 is a prime number so it only consists of 2 factors. In this article, we will take a look at these factors and determine how to evaluate them.  

Factors of 157

Here are the factors of number 157.

Factors of 157: 1, 157

Negative Factors of 157

The negative factors of 157 are similar to its positive factors, just with a negative sign.

Negative Factors of 157: -1 and -157

Prime Factorization of 157

The prime factorization of 157 is the way of expressing its prime factors in the product form.

 

Prime Factorization: 1 x 157

In this article, we will learn about the factors of 157 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 157?

The factors of 157 are 1 and 157. All of these numbers are the factors as they do not leave any remainder when divided by 157.

The factors of 157 are classified as prime numbers and composite numbers. The prime factors of the number 157 can be determined using the technique of prime factorization.

How To Find the Factors of 157?

You can find the factors of 157 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it 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 157, create a list containing the numbers that are exactly divisible by 157 with zero remainders. One important thing to note is that 1 and 157 are the 157’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 157 are determined as follows:

\[\dfrac{157}{1} = 157\]

\[\dfrac{157}{157} = 1\]

Therefore, 1 and 157 are the factors of 157.

Total Number of Factors of 157

For 157 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 157. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the 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 157 is given as:

The factorization of 157 is 1 x 157.

The exponent of 1 and 157 is 1.

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

Therefore, the total number of factors of 157 is 4, where 2 are positive factors and 2 are negative factors.

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 which is the smallest prime factor.

Factors of 157 by Prime Factorization

The number 157 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 157 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 157, 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 157 can be expressed as:

157 = 1 x 157

Factors of 157 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.

 

For 157, the factor pairs can be found as:

 1 x 157 = 157

The possible factor pair of 157 is given as (1, 157).

All these numbers in pairs, when multiplied, give 157 as the product.

The negative factor pairs of 157 are given as:

-1 x -157 = 157

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 -157 are called negative factors of 157.

The list of all the factors of 157 including positive as well as negative numbers is given below.

Factor list of 157: 1, -1, 157, and -157

Factors of 157 Solved Examples

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

Example 1

How many factors of 157 are there?

Solution

The total number of Factors of 157 is 2.

Factors of 157 are 1 and 157.

Example 2

Find the factors of 157 using prime factorization.

Solution

The prime factorization of 157 is given as:

157 $\div$ 157 = 1 

So the prime factorization of 157 can be written as:

1 x 157 = 157

Factors of 156 | Factors List| Factors of 158

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