Factors of 151: Prime Factorization, Methods, and Examples

The factors of 151 are the numbers that produce zero as a remainder whenever 151 is divided from them. Such divisors and their whole number quotients both act as factors.

The factors of 151 are only 2 in number as the number 151 is a prime number. In this article, we will take a look at these factors and how to determine them. 

Factors of 151

Here are the factors of number 151.

Factors of 151: 1, 151

Negative Factors of 151

The negative factors of 151 are similar to its positive factors, just with a negative sign.

Negative Factors of 151: -1 and -151

Prime Factorization of 151

The prime factorization of 151 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 151

In this article, we will learn about the factors of 151 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 151?

The factors of 151 are 1 and 151. All of these numbers are the factors as they do not leave any remainder when divided by 151.

The factors of 151 are classified as prime numbers and composite numbers. The prime factors of the number 151 can be determined using the technique of prime factorization.

How To Find the Factors of 151?

You can find the factors of 151 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 151, create a list containing the numbers that are exactly divisible by 151 with zero remainders. One important thing to note is that 1 and 151 are the 151’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 151 are determined as follows:

\[\dfrac{151}{1} = 151\]

\[\dfrac{151}{151} = 1\]

Therefore, 1 and 151 are the factors of 151.

Total Number of Factors of 151

For 151 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 151. 

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 151 is given as:

The factorization of 151 is 1 x 151.

The exponent of 1 and 151 is 151.

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

Therefore, the total number of factors of 151 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 151 by Prime Factorization

The number 151 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 151 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 151, 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 151 can be expressed as:

151 = 1 x 151

Factors of 151 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 151, the factor pairs can be found as:

1 x 151 = 151

The possible factor pairs of 151 are given as (1, 151).

All these numbers in pairs, when multiplied, give 151 as the product.

The negative factor pairs of 151 are given as:

-1 x -151 = 151

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 -151 are called negative factors of 151.

The list of all the factors of 151 including positive as well as negative numbers is given below.

Factor list of 151: 1, -1, 151, and -151

Factors of 151 Solved Examples

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

Example 1

How many factors of 151 are there?

Solution

The total number of Factors of 151 is 2.

Factors of 151 are 1 and 151.

Example 2

Find the sum of the factors of 1 and 151.

Solution

The sum of the factors of 151 are:

Sum = 1 + 151

Sum = 152

The sum of factors of 151 is 152. 

Factors of 150 |Factors List | Factors of 152