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Factors of 348: Prime Factorization, Methods, and Examples

In this article, we see factors of number 348 as it is divisible by 2 so it is an even number. When calculating the factor of 348 it gives those factors which are usually integers and divisible by the number 348 completely and gives no residue.

 In this case, 348 is a composite number we see this thing in detail below as well.

Factors of 348

Here are the factors of number 348.

Factors of 348: 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348

Negative Factors of 348

The negative factors of 348 are similar to their positive aspects, just with a negative sign.

Negative Factors of 348: -1, -2, -3, -4, -6, -12, -29, -58, -87, -116, -174, and -348

Prime Factorization of 348

The prime factorization of 348 is the way of expressing its prime factors in the product form.

Prime Factorization:  2 x 2 x 3 x 29

In this article, we will learn about the factors of 348 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 348?

The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348. These numbers are the factors as they do not leave any remainder when divided by 348.

The factors of 348 are classified as prime numbers and composite numbers. The prime factors of the number 348 can be determined using the prime factorization technique.

How To Find the Factors of 348?

You can find the factors of 348 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, 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 348, create a list containing the numbers that are exactly divisible by 348 with zero remainders. One important thing to note is that 1 and 348 are the 348’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 348 are determined as follows:

\[\dfrac{348}{1} = 348\]

\[\dfrac{348}{2} = 174\]

\[\dfrac{348}{3} = 116\]

\[\dfrac{348}{4} = 87\]

\[\dfrac{348}{6} = 58\]

\[\dfrac{348}{12} = 29\]

\[\dfrac{348}{29} = 12\]

\[\dfrac{348}{58} = 6\]

\[\dfrac{348}{87} = 4\]

\[\dfrac{348}{116} = 3\]

\[\dfrac{348}{174} = 2\]

\[\dfrac{348}{348} = 1\]

Therefore, 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348 are the factors of 348.

Total Number of Factors of 348

For 348, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 348. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime 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 348 is given as:

Factorization of 348 is 1 x 2 x 2 x 3 x 29.

The exponent of 1 x 2 x 2 x 3 x 29 is 1.

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 348 is 24. Twelve are positive, and twelve factors are negative.

Important Notes

Here are some essential 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, the smallest prime factor.

Factors of 348 by Prime Factorization

The number 348 is a composite. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 348 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 348, start dividing by its most minor 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 348 can be expressed as:

348 = 2 x 2 x 3 x 29

Factors of 348 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 348, the factor pairs can be found as:

1 x 348 = 348

2 x 174 = 348 

3 x 116 = 348

4 x 87 = 348 

6 x 58 = 348

12 x 29 = 348

 

The possible factor pairs of 348 are given as (1, 348), (2, 174), (3, 116), (4, 87), (6, 58) and (12, 29).

All these numbers in pairs, when multiplied, give 348 as the product.

The negative factor pairs of 348 are given as:

-1 x -348 = 348

-2 x -174 = 348 

-3 x -116 = 348

-4 x -87 = 348 

-6 x -58 = 348

-12 x -29 = 348

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, -3, -4, -6, -12, -29, -58, -87, -116, -174, and -348 are called negative factors of 348.

The list of all the factors of 348, including positive as well as negative numbers, is given below.

Factor list of 348: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12, 29, -29, 58, -58, 87, -87, 116, -116, 174, -174, 348 and -348

Factors of 348 Solved Examples

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

Example 1

How many factors of 348 are there?

Solution

The total number of Factors of 348 is m.

Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348.

Example 2

Find the factors of 348 using prime factorization.

Solution

The prime factorization of 348 is given as:

348 $\div$ 2 = 174 

174 $\div$ 2 = 87 

87 $\div$ 3 = 29

29 $\div$ 29 = 1 

So the prime factorization of 348 can be written as:

2 x 2 x 3 x 29 = 348

Factors of 347|Factors List| Factors of 349

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