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Factors of 208

Factors of 208 are numbers that, when multiplied in pairs give the product as 208. There are 10 factors of 208, of which the following are its prime factors 2, 13. The sum of all factors of 208 is 434.

  • All Factors of 208: 1, 2, 4, 8, 13, 16, 26, 52, 104 and 208
  • Negative Factors of 208: -1, -2, -4, -8, -13, -16, -26, -52, -104 and -208
  • Prime Factors of 208: 2, 13
  • Prime Factorization of 208: 24 × 131
  • Sum of Factors of 208: 434
1. What Are the Factors of 208?
2. Factors of 208 by Prime Factorization
3. Factors of 208 in Pairs
4. FAQs on Factors of 208
Factors of 208

What are Factors of 208?

Factors of 208 are pairs of those numbers whose products result in 208. These factors are either prime numbers or composite numbers.

How to Find the Factors of 208?

To find the factors of 208, we will have to find the list of numbers that would divide 208 without leaving any remainder.

  • 208/13 = 16; therefore, 13 is a factor of 208 and 16 is also a factor of 208.
  • 208/52 = 4; therefore, 52 is a factor of 208 and 4 is also a factor of 208.
Similarly we can find other factors. Hence, the factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.

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Factors of 208 by Prime Factorization

The number 208 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 208. The first step is to divide the number 208 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 208 ÷ 2 = 104
  • 104 ÷ 2 = 52
  • 52 ÷ 2 = 26
  • 26 ÷ 2 = 13

Further dividing 13 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 13 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 208 can be written as 24 × 131 where 2, 13 are prime.

 

Factors of 208 in Pairs

Pair factors of 208 are the pairs of numbers that when multiplied give the product 208. The factors of 208 in pairs are:

  • 1 × 208 = (1, 208)
  • 2 × 104 = (2, 104)
  • 4 × 52 = (4, 52)
  • 8 × 26 = (8, 26)
  • 13 × 16 = (13, 16)

Negative pair factors of 208 are:

  • -1 × -208 = (-1, -208)
  • -2 × -104 = (-2, -104)
  • -4 × -52 = (-4, -52)
  • -8 × -26 = (-8, -26)
  • -13 × -16 = (-13, -16)

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

Factors of 208 Solved Examples

  1. Example 1: How many factors are there for 208?

    Solution:

    The factors of 208 are too many, therefore if we can find the prime factorization of 208, 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 208 = 24 × 131
    Therefore, the total number of factors are (4 + 1) × (1 + 1) = 5 × 2 = 10

  2. Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 208 and 154.

    Solution:

    The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208 and factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154.

    Therefore, the Least Common Multiple of 208 and 154 is 16016 and Greatest Common Divisor (GCD) of 208 and 154 is 2.

  3. Example 3: Find if 1, 2, 8, 52, 126 and 208 are factors of 208.

    Solution:

    When we divide 208 by 126 it leaves a remainder. Therefore, the number 126 is not a factor of 208. All numbers except 126 are factors of 208.

  4. Example 4: Find the product of all the prime factors of 208.

    Solution:

    Since, the prime factors of 208 are 2, 13. Therefore, the product of prime factors = 2 × 13 = 26.

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FAQs on Factors of 208

What are the Factors of 208?

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208 and its negative factors are -1, -2, -4, -8, -13, -16, -26, -52, -104, -208.

What is the Sum of all Factors of 208?

Sum of all factors of 208 = (24 + 1 - 1)/(2 - 1) × (131 + 1 - 1)/(13 - 1) = 434

What are Pair Factors of 208?

The pair factors of 208 are (1, 208), (2, 104), (4, 52), (8, 26), (13, 16).

What is the Greatest Common Factor of 208 and 122?

The factors of 208 and 122 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208 and 1, 2, 61, 122 respectively.

Common factors of 208 and 122 are [1, 2].

Hence, the Greatest Common Factor (GCF) of 208 and 122 is 2.

What are the Common Factors of 208 and 157?

Since, the factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208 and factors of 157 are 1, 157. Hence, 208 and 157 have only one common factor which is 1. Therefore, 208 and 157 are co-prime.

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