Given Numbers: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000
Identify the Prime Factors of 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1,000 by Prime Factorization
Identify the Prime Factors of 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1,000 by Prime Factorization
- Prime Factorization of 100: 100 = 2 x 2 x 5 x 5 = 22 x 52
- Prime Factorization of 200: 200 = 2 x 2 x 2 x 5 x 5 = 23 x 52
- Prime Factorization of 300: 300 = 2 x 2 x 3 x 5 x 5 = 22 x 31 x 52
- Prime Factorization of 400: 400 = 2 x 2 x 2 x 2 x 5 x 5 = 24 x 52
- Prime Factorization of 500: 500 = 2 x 2 x 5 x 5 x 5 = 22 x 53
- Prime Factorization of 600: 600 = 2 x 2 x 2 x 3 x 5 x 5 = 23 x 31 x 52
- Prime Factorization of 700: 700 = 2 x 2 x 5 x 5 x 7 = 22 x 52 x 71
- Prime Factorization of 800: 800 = 2 x 2 x 2 x 2 x 2 x 5 x 5 = 25 x 52
- Prime Factorization of 900: 900 = 2 x 2 x 3 x 3 x 5 x 5 = 22 x 32 x 52
- Prime Factorization of 1,000: 1,000 = 2 x 2 x 2 x 5 x 5 x 5 = 23 x 53
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 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1,000
Determine the least number of occurrences of 2 and 5 among the Prime Factorizations:
- 2 occurs at least 2 times in each Prime Factorization
- 5 occurs at least 2 times in each Prime Factorization
As a result, the Greatest Common Factor (GCF) of 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1,000 is equal to 2 x 2 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(100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000) = 22 x 52 = 2 x 2 x 5 x 5
- GCF(100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000) = 4 x 25
- GCF(100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000) = 100
Therefore, the Greatest Common Factor of 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1,000 by Prime Factorization = 100