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Factors of 308

Factors of 308 are integers that can be divided evenly into 308. There are overall 12 factors of 308 among which 308 is the biggest factor and its prime factors are 2, 7, 11. The Prime Factorization of 308 is 22 × 71 × 111.

  • All Factors of 308: 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154 and 308
  • Prime Factors of 308: 2, 7, 11
  • Prime Factorization of 308: 22 × 71 × 111
  • Sum of Factors of 308: 672
1. What Are the Factors of 308?
2. Factors of 308 by Prime Factorization
3. Factors of 308 in Pairs
4. FAQs on Factors of 308
Factors of 308

What are Factors of 308?

Factors of 308 are pairs of those numbers whose products result in 308. These factors are either prime numbers or composite numbers.

How to Find the Factors of 308?

To find the factors of 308, we will have to find the list of numbers that would divide 308 without leaving any remainder.

  • 308/14 = 22; therefore, 14 is a factor of 308 and 22 is also a factor of 308.
  • 308/28 = 11; therefore, 28 is a factor of 308 and 11 is also a factor of 308.
Similarly we can find other factors. Hence, the factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.

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Factors of 308 by Prime Factorization

The number 308 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 308. The first step is to divide the number 308 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 308 ÷ 2 = 154
  • 154 ÷ 2 = 77

Further dividing 77 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 77 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 308 can be written as 22 × 71 × 111 where 2, 7, 11 are prime.

 

Factors of 308 in Pairs

Pair factors of 308 are the pairs of numbers that when multiplied give the product 308. The factors of 308 in pairs are:

  • 1 × 308 = (1, 308)
  • 2 × 154 = (2, 154)
  • 4 × 77 = (4, 77)
  • 7 × 44 = (7, 44)
  • 11 × 28 = (11, 28)
  • 14 × 22 = (14, 22)

Negative pair factors of 308 are:

  • -1 × -308 = (-1, -308)
  • -2 × -154 = (-2, -154)
  • -4 × -77 = (-4, -77)
  • -7 × -44 = (-7, -44)
  • -11 × -28 = (-11, -28)
  • -14 × -22 = (-14, -22)

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

Factors of 308 Solved Examples

  1. Example 1: How many factors are there for 308?

    Solution:

    The factors of 308 are too many, therefore if we can find the prime factorization of 308, 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 308 = 22 × 71 × 111
    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 and Highest Common Factor (HCF) of 308 and 197.

    Solution:

    The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308 and factors of 197 are 1, 197.

    Therefore, the Least Common Multiple of 308 and 197 is 60676 and Highest Common Factor (HCF) of 308 and 197 is 1.

  3. Example 3: Find if 4, 7, 22, 44, 77, 228 and 308 are factors of 308.

    Solution:

    When we divide 308 by 228 it leaves a remainder. Therefore, the number 228 is not a factor of 308. All numbers except 228 are factors of 308.

  4. Example 4: Find the product of all the prime factors of 308.

    Solution:

    Since, the prime factors of 308 are 2, 7, 11. Therefore, the product of prime factors = 2 × 7 × 11 = 154.

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FAQs on Factors of 308

What are the Factors of 308?

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308 and its negative factors are -1, -2, -4, -7, -11, -14, -22, -28, -44, -77, -154, -308.

What is the Sum of Factors of 308?

Sum of all factors of 308 = (22 + 1 - 1)/(2 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 672

What Numbers are the Prime Factors of 308?

The prime factors of 308 are 2, 7, 11.

What is the Greatest Common Factor of 308 and 137?

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308 and the factors of 137 are 1, 137. 308 and 137 have only one common factor which is 1. This implies that 308 and 137 are co-prime.

Hence, the Greatest Common Factor (GCF) of 308 and 137 is 1.

How Many Factors of 308 are also common to the Factors of 149?

Since, the factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308 and factors of 149 are 1, 149. Hence, 308 and 149 have only one common factor which is 1. Therefore, 308 and 149 are co-prime.

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