Greatest Common Factor of 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000 and 10,000 by Prime Factorization

Given Numbers: 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000
Identify the Prime Factors of 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000 and 10,000 by Prime Factorization
  • Prime Factorization of 1,000: 1,000 = 2 x 2 x 2 x 5 x 5 x 5 = 23 x 53
  • Prime Factorization of 2,000: 2,000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 = 24 x 53
  • Prime Factorization of 3,000: 3,000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 = 23 x 31 x 53
  • Prime Factorization of 4,000: 4,000 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 = 25 x 53
  • Prime Factorization of 5,000: 5,000 = 2 x 2 x 2 x 5 x 5 x 5 x 5 = 23 x 54
  • Prime Factorization of 6,000: 6,000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 = 24 x 31 x 53
  • Prime Factorization of 7,000: 7,000 = 2 x 2 x 2 x 5 x 5 x 5 x 7 = 23 x 53 x 71
  • Prime Factorization of 8,000: 8,000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 = 26 x 53
  • Prime Factorization of 9,000: 9,000 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5 = 23 x 32 x 53
  • Prime Factorization of 10,000: 10,000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 = 24 x 54

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 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000 and 10,000

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

  • 2 occurs at least 3 times in each Prime Factorization
  • 5 occurs at least 3 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000 and 10,000 is equal to 2 x 2 x 2 x 5 x 5 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(1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000) = 23 x 53 = 2 x 2 x 2 x 5 x 5 x 5
  • GCF(1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000) = 8 x 125
  • GCF(1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000) = 1,000

Therefore, the Greatest Common Factor of 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000 and 10,000 by Prime Factorization = 1,000

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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