 # Factors of 154: Prime Factorization, Methods, and Examples

The factors of 154 are the numbers upon which the number 154 is completely divisible. For such numbers, both the divisors and the whole number quotients act as the factors. The factors of 154 are multiple in existence since the number 154 is even composite. They can be determined through various techniques.

### Factors of 154

Here are the factors of number 154.

Factors of 154: 1, 2, 7, 11, 14, 22, 77, 154

### Negative Factors of 154

The negative factors of 154 are similar to its positive factors, just with a negative sign.

Negative Factors of 154: -1, -2, -7, -11, -14, -22, -77, and -154

### Prime Factorization of 154

The prime factorization of 154 is the way of expressing its prime factors in the product form. Prime Factorization: 2 x 7 x 11

In this article, we will learn about the factors of 154 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 154?

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, and 154. All of these numbers are the factors as they do not leave any remainder when divided by 154.

The factors of 154 are classified as prime numbers and composite numbers. The prime factors of the number 154 can be determined using the technique of prime factorization.

## How To Find the Factors of 154?

You can find the factors of 154 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 154, create a list containing the numbers that are exactly divisible by 154 with zero remainders. One important thing to note is that 1 and 154 are the 154’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 154 are determined as follows:

$\dfrac{154}{1} = 154$

$\dfrac{154}{2} = 77$

$\dfrac{154}{7} = 22$

$\dfrac{154}{11} = 14$

$\dfrac{154}{14} = 11$

$\dfrac{154}{22} = 7$

$\dfrac{154}{77} = 2$

$\dfrac{154}{154} =1$

Therefore, 1, 2, 7, 11, 14, 22, 77, and 154 are the factors of 154.

### Total Number of Factors of 154

For 154 there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 154.

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 154 is given as:

Factorization of 154 is 1 x 2 x 7 x 11

The exponent of all these factors is 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 154 is 16, where 8 are positive factors and 8 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 which is the smallest prime factor.

## Factors of 154 by Prime Factorization

The number 154 is composite. 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 154 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 154, 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 154 can be expressed as:

154 = 2 x 7 x 11

## Factors of 154 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 154, the factor pairs can be found as:

1 x 154 = 154

2 x 77 = 154

7 x 22 = 154

11 x 14 = 154

The possible factor pairs of 154 are given as (1, 154), (2, 77), (7, 22), and(11, 14).

All these numbers in pairs, when multiplied, give 154 as the product.

The negative factor pairs of 154 are given as:

-1 x -154 = 154

-2 x -77 = 154

-7 x -22 = 154

– 11 x -14 = 154

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, -7, -11, -14, -22, -77, and -154 are called negative factors of 154.

The list of all the factors of 154 including positive as well as negative numbers is given below.

Factor list of 154: 1, -1, 2, -2, 7, -7, 11, -11, 14, -14, 22, -22, 77, -77, 154, and -154

## Factors of 154 Solved Examples

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

### Example 1

How many factors of 154 are there?

### Solution

The total number of Factors of 154 is 8.

Factors of 154 are 1, 2, 7, 11, 14, 22, 77, and 154.

### Example 2

Find the factors of 154 using prime factorization.

### Solution

The prime factorization of 154 is given as:

154 $\div$ 2 = 77

77 $\div$ 7 = 11

11 $\div$ 11 = 1

So the prime factorization of 154 can be written as:

2 x 7 x 11 = 154