What is the Greatest Common Factor of 47586 and 47600?

Greatest common factor (GCF) of 47586 and 47600 is 14.

GCF(47586,47600) = 14

We will now calculate the prime factors of 47586 and 47600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47586 and 47600.

How to find the GCF of 47586 and 47600?

We will first find the prime factorization of 47586 and 47600. After we will calculate the factors of 47586 and 47600 and find the biggest common factor number .

Step-1: Prime Factorization of 47586

Prime factors of 47586 are 2, 3, 7, 11, 103. Prime factorization of 47586 in exponential form is:

47586 = 2¹ × 3¹ × 7¹ × 11¹ × 103¹

Step-2: Prime Factorization of 47600

Prime factors of 47600 are 2, 5, 7, 17. Prime factorization of 47600 in exponential form is:

47600 = 2⁴ × 5² × 7¹ × 17¹

Step-3: Factors of 47586

List of positive integer factors of 47586 that divides 47586 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 103, 154, 206, 231, 309, 462, 618, 721, 1133, 1442, 2163, 2266, 3399, 4326, 6798, 7931, 15862, 23793

Step-4: Factors of 47600

List of positive integer factors of 47600 that divides 47586 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 25, 28, 34, 35, 40, 50, 56, 68, 70, 80, 85, 100, 112, 119, 136, 140, 170, 175, 200, 238, 272, 280, 340, 350, 400, 425, 476, 560, 595, 680, 700, 850, 952, 1190, 1360, 1400, 1700, 1904, 2380, 2800, 2975, 3400, 4760, 5950, 6800, 9520, 11900, 23800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47586 and 47600. The biggest common factor number is the GCF number.
So the greatest common factor 47586 and 47600 is 14.

Also check out the Least Common Multiple of 47586 and 47600