Greatest Common Factor of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 by Prime Factorization

Given Numbers: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Identify the Prime Factors of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 by Prime Factorization
  • Prime Factorization of 10: 10 = 2 x 5 = 21 x 51
  • Prime Factorization of 20: 20 = 2 x 2 x 5 = 22 x 51
  • Prime Factorization of 30: 30 = 2 x 3 x 5 = 21 x 31 x 51
  • Prime Factorization of 40: 40 = 2 x 2 x 2 x 5 = 23 x 51
  • Prime Factorization of 50: 50 = 2 x 5 x 5 = 21 x 52
  • Prime Factorization of 60: 60 = 2 x 2 x 3 x 5 = 22 x 31 x 51
  • Prime Factorization of 70: 70 = 2 x 5 x 7 = 21 x 51 x 71
  • Prime Factorization of 80: 80 = 2 x 2 x 2 x 2 x 5 = 24 x 51
  • Prime Factorization of 90: 90 = 2 x 3 x 3 x 5 = 21 x 32 x 51
  • Prime Factorization of 100: 100 = 2 x 2 x 5 x 5 = 22 x 52

Determine the Prime Factor(s) that are common to the Prime Factorization of each number:

  • 2 and 5 are Prime Factors common to the Prime Factorizations of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100

Determine the least number of occurrences of 2 and 5 among the Prime Factorizations:

  • 2 occurs at least 1 time in each Prime Factorization
  • 5 occurs at least 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 is equal to 2 x 5, which equals the product of 2 and 5 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

  • GCF(10, 20, 30, 40, 50, 60, 70, 80, 90, 100) = 21 x 51
  • GCF(10, 20, 30, 40, 50, 60, 70, 80, 90, 100) = 2 x 5
  • GCF(10, 20, 30, 40, 50, 60, 70, 80, 90, 100) = 10

Therefore, the Greatest Common Factor of 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 by Prime Factorization = 10

The solution above and other related solutions were provided by the GCF by Prime Factorization Application.

Find the Greatest Common Factor by Prime Factorization

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