 # Factors of 153: Prime Factorization, Methods, and Examples

The factors of 153 are the numbers that yield zero as a remainder whenever 153 is divided from them. These numbers also produce a whole number quotient.

The factors of 153 can be found through two major techniques, one is the division method and the second is the prime factorization. In this article, we will take a comprehensive look at these techniques.

### Factors of 153

Here are the factors of number 153.

Factors of 153: 1, 3, 9, 17, 51, and 153

### Negative Factors of 153

The negative factors of 153 are similar to its positive factors, just with a negative sign.

Negative Factors of 153: -1, -3, -9, -17, -51 and -153

### Prime Factorization of 153

The prime factorization of 153 is the way of expressing its prime factors in the product form.

$\text{Prime Factorization} = 3^{2} \times 17$

In this article, we will learn about the factors of 153 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 153?

The factors of 153 are 1, 3, 9, 17, 51, and 153. All of these numbers are the factors as they do not leave any remainder when divided by 153.

The factors of 153 are classified as prime numbers and composite numbers. The prime factors of the number 153 can be determined using the technique of prime factorization.

## How To Find the Factors of 153?

You can find the factors of 153 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 153, create a list containing the numbers that are exactly divisible by 153 with zero remainders. One important thing to note is that 1 and 153 are the 153’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 153 are determined as follows:

$\dfrac{153}{1} = 153$

$\dfrac{153}{3} = 51$

$\dfrac{153}{9} = 17$

$\dfrac{153}{17} = 9$

$\dfrac{153}{51} = 3$

$\dfrac{153}{153} = 1$

Therefore, 1, 3, 9, 17, 51, and 153 are the factors of 153.

### Total Number of Factors of 153

For 153 there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 153.

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 153 is given as:

$Factorization = 1 \times 3^{2} \times 17$

The exponent of 1 and 17 is 1, whereas that of 3 is 2.

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

Therefore, the total number of factors of 153 is 12 where 6 are positive and 6 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 153 by Prime Factorization

The number 153 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 153 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 153, 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 153 can be expressed as:

$153 = 3^{2} \times 17$

## Factors of 153 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 153, the factor pairs can be found as:

$1 \times 153 = 153$

$3 \times 51 = 153$

$9 \times 17 = 153$

The possible factor pairs of 153 are given as (1, 153), (3, 51), and (9, 17).

All these numbers in pairs, when multiplied, give 153 as the product.

The negative factor pairs of 153 are given as:

$-1 \times -153 = 153$

$-3 \times -51 = 153$

$-9 \times -17 = 153$

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, -3, -9, -17, -51, and -153 are called negative factors of 153.

The list of all the factors of 153 including positive as well as negative numbers is given below.

Factor list of 153: 1, -1, 3, -3, 9, -9, 17, -17, -51, -51, 153, and -153

## Factors of 153 Solved Examples

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

### Example 1

How many factors of 153 are there?

### Solution

The total number of Factors of 153 is 6.

Factors of 153 are 1, 3, 9, 17, 51, and 153.

### Example 2

Find the factors of 153 using prime factorization.

### Solution

The prime factorization of 153 is given as:

$153 \div 3 = 51$

$51 \div 3 = 17$

$17 \div 17 = 1$

So the prime factorization of 153 can be written as:

$3^{2} \times 17 = 153$