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Factors of 142: Prime Factorization, Methods, and Examples

The factors of 142 are the numbers upon which 142 is completely divisible. In other words, these are the numbers that produce zero as a remainder after division with 142.

The factors of 142 can be determined through various methods. Since 142 is an even composite factor so it has multiple factors. 

Factors of 142

Here are the factors of number 142.

Factors of X: 1, 2, 71, 142

Negative Factors of 142

The negative factors of 142 are similar to its positive factors, just with a negative sign.

Negative Factors of 142: -1, -2, -71, and -142

Prime Factorization of 142

The prime factorization of 142 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 71

In this article, we will learn about the factors of 142 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 142?

The factors of 142 are 1, 2, 71, and 142. All of these numbers are the factors as they do not leave any remainder when divided by 142.

The factors of 142 are classified as prime numbers and composite numbers. The prime factors of the number 142 can be determined using the technique of prime factorization.

How To Find the Factors of 142?

You can find the factors of 142 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 142, create a list containing the numbers that are exactly divisible by 142 with zero remainders. One important thing to note is that 1 and 142 are the 142’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 142 are determined as follows:

\[\dfrac{142}{1} = 142\]

\[\dfrac{142}{2} = 71\]

\[\dfrac{142}{71} = 2\]

\[\dfrac{142}{142} = 1\]

Therefore, 1, 2, 71, and 142 are the factors of 142.

Total Number of Factors of 142

For 142 there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 142. 

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 142 is given as:

Factorization of 142 is 1 x 2 x 71.

The exponent of 1, 2, and 71 is 1.

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

Therefore, the total number of factors of 142 is 8, where there are 4 positive factors and 4 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 142 by Prime Factorization

The number 142 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 142 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 142, 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 142 can be expressed as:

\[  142 = 2 \times 71\]

Factors of 142 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 142, the factor pairs can be found as:

\[ 1 \times 142 = 142 \]

\[ 2 \times 71 = 142 \]

The possible factor pairs of 142 are given as (1, 142) and (2, 71).

All these numbers in pairs, when multiplied, give 142 as the product.

The negative factor pairs of 142 are given as:

\[ -1 \times -142 = 142 \]

\[ -2 \times -71 = 142 \]

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, -71, and -142 are called negative factors of 142.

The list of all the factors of 142 including positive as well as negative numbers is given below.

Factor list of 142: 1, -1, 2, -2, 71, -71, 142, and -142

Factors of 142 Solved Examples

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

Example 1

How many factors of 142 are there?

Solution

The total number of Factors of 142 is 4.

Factors of 142 are 1, 2, 71, and 142.

Example 2

Find the factors of 142 using prime factorization.

Solution

The prime factorization of 142 is given as:

\[ 142 \div 2 = 71 \]

\[ 71 \div 71 = 1 \]

So the prime factorization of 142 can be written as:

\[ 2 \times 71 = 142 \]

Factors of 141Factors List | Factors of 143

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