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Factors of 145: Prime Factorization, Methods, and Examples

The factors of 145 are the numbers that completely divide 145 and leave zero as the remainder behind. These numbers also leave a whole number quotient which also acts as the factor.

Since the number 145 is an odd composite number, so it consists of multiple factors. Let’s take a look at these factors and have to determine them through various techniques. 

Factors of 145 

Here are the factors of number 145.

Factors of 145: 1, 5, 29, 145

Negative Factors of 145

The negative factors of 145 are similar to its positive factors, just with a negative sign.

Negative Factors of 145: -1, -5, -29, and -145

Prime Factorization of 145

The prime factorization of 145 is the way of expressing its prime factors in the product form.

Prime Factorization: 5 x 29 

In this article, we will learn about the factors of 145 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 145?

The factors of 145 are 1, 5, 29, and 145. All of these numbers are the factors as they do not leave any remainder when divided by 145.

The factors of 145 are classified as prime numbers and composite numbers. The prime factors of the number 145 can be determined using the technique of prime factorization.

How To Find the Factors of 145?

You can find the factors of 145 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 145, create a list containing the numbers that are exactly divisible by 145 with zero remainders. One important thing to note is that 1 and 145 are the 145’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 145 are determined as follows:

\[\dfrac{145}{1} = 145\]

\[\dfrac{145}{5} = 29\]

\[\dfrac{145}{29} = 5\]

\[\dfrac{145}{145} = 1\]

Therefore, 1, 5, 29, and 145 are the factors of 145.

Total Number of Factors of 145

For 145 there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 145. 

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 145 is given as:

Factorization of 145 is 1 x 5 x 29.

The exponent of 1, 5, and 29 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 145 is 8, where 4 are positive factors are 4 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 145 by Prime Factorization

The number 145 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 145 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 145, 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 145 can be expressed as:

\[  145 = 5 \times 29\]

Factors of 145 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 145, the factor pairs can be found as:

\[ 1 \times 145 = 145 \]

\[ 5 \times 29 = 145 \]

The possible factor pairs of 145 are given as (1, 145) and (5, 29).

All these numbers in pairs, when multiplied, give 145 as the product.

The negative factor pairs of 145 are given as:

\[ -1 \times -145 = 145 \]

\[ -5 \times -29 = 145 \]

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, -5, -29, and -145 are called negative factors of 145.

The list of all the factors of 145 including positive as well as negative numbers is given below.

Factor list of 145: 1, -1, 5, -5, 29, -29, 145, and -145

Factors of 145 Solved Examples

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

Example 1

How many factors of 145 are there?

Solution

The total number of Factors of 145 is 4.

Factors of 145 are 1, 5, 29, and 145.

Example 2

Find the factors of 145 using prime factorization.

Solution

The prime factorization of 145 is given as:

\[ 145 \div 5 = 29 \]

\[ 29 \div 29 = 1 \]

So the prime factorization of 145 can be written as:

\[ 5 \times 29 = 145 \]

Factors of 144 | Factors List| Factors of 146

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