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
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