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Factors of 348

Factors of 348 are the list of integers that we can split evenly into 348. There are overall 12 factors of 348 among which 348 is the biggest factor and its prime factors are 2, 3, 29. The Prime Factorization of 348 is 22 × 31 × 291.

  • All Factors of 348: 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174 and 348
  • Prime Factors of 348: 2, 3, 29
  • Prime Factorization of 348: 22 × 31 × 291
  • Sum of Factors of 348: 840
1. What Are the Factors of 348?
2. Factors of 348 by Prime Factorization
3. Factors of 348 in Pairs
4. FAQs on Factors of 348
Factors of 348

What are Factors of 348?

Factors of 348 are pairs of those numbers whose products result in 348. These factors are either prime numbers or composite numbers.

How to Find the Factors of 348?

To find the factors of 348, we will have to find the list of numbers that would divide 348 without leaving any remainder.

  • 348/116 = 3; therefore, 116 is a factor of 348 and 3 is also a factor of 348.
  • 348/2 = 174; therefore, 2 is a factor of 348 and 174 is also a factor of 348.
Similarly we can find other factors. Hence, the factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348.

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Factors of 348 by Prime Factorization

The number 348 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 348. The first step is to divide the number 348 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 348 ÷ 2 = 174
  • 174 ÷ 2 = 87

Further dividing 87 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 87 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 348 can be written as 22 × 31 × 291 where 2, 3, 29 are prime.

 

Factors of 348 in Pairs

Pair factors of 348 are the pairs of numbers that when multiplied give the product 348. The factors of 348 in pairs are:

  • 1 × 348 = (1, 348)
  • 2 × 174 = (2, 174)
  • 3 × 116 = (3, 116)
  • 4 × 87 = (4, 87)
  • 6 × 58 = (6, 58)
  • 12 × 29 = (12, 29)

Negative pair factors of 348 are:

  • -1 × -348 = (-1, -348)
  • -2 × -174 = (-2, -174)
  • -3 × -116 = (-3, -116)
  • -4 × -87 = (-4, -87)
  • -6 × -58 = (-6, -58)
  • -12 × -29 = (-12, -29)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 348 Solved Examples

  1. Example 1: How many factors are there for 348?

    Solution:

    The factors of 348 are too many, therefore if we can find the prime factorization of 348, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 348 = 22 × 31 × 291
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 348 and 216.

    Solution:

    The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348 and factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.

    Therefore, the Least Common Multiple (LCM) of 348 and 216 is 6264 and Greatest Common Divisor (GCD) of 348 and 216 is 12.

  3. Example 3: Find if 2, 4, 29, 58, 95, 116 and 348 are factors of 348.

    Solution:

    When we divide 348 by 95 it leaves a remainder. Therefore, the number 95 is not a factor of 348. All numbers except 95 are factors of 348.

  4. Example 4: Find the product of all the prime factors of 348.

    Solution:

    Since, the prime factors of 348 are 2, 3, 29. Therefore, the product of prime factors = 2 × 3 × 29 = 174.

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FAQs on Factors of 348

What are the Factors of 348?

The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348 and its negative factors are -1, -2, -3, -4, -6, -12, -29, -58, -87, -116, -174, -348.

What is the Sum of all the Factors of 348?

Sum of all factors of 348 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (291 + 1 - 1)/(29 - 1) = 840

What numbers are the Pair Factors of 348?

The pair factors of 348 are (1, 348), (2, 174), (3, 116), (4, 87), (6, 58), (12, 29).

What is the Greatest Common Factor of 348 and 38?

The factors of 348 and 38 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348 and 1, 2, 19, 38 respectively.

Common factors of 348 and 38 are [1, 2].

Hence, the GCF of 348 and 38 is 2.

How Many Factors of 348 are also common to the Factors of 308?

Since, the factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348 and the factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.
Hence, [1, 2, 4] are the common factors of 348 and 308.

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