What is the Greatest Common Factor of 49380 and 49400?

Greatest common factor (GCF) of 49380 and 49400 is 20.

GCF(49380,49400) = 20

We will now calculate the prime factors of 49380 and 49400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49380 and 49400.

How to find the GCF of 49380 and 49400?

We will first find the prime factorization of 49380 and 49400. After we will calculate the factors of 49380 and 49400 and find the biggest common factor number .

Step-1: Prime Factorization of 49380

Prime factors of 49380 are 2, 3, 5, 823. Prime factorization of 49380 in exponential form is:

49380 = 2² × 3¹ × 5¹ × 823¹

Step-2: Prime Factorization of 49400

Prime factors of 49400 are 2, 5, 13, 19. Prime factorization of 49400 in exponential form is:

49400 = 2³ × 5² × 13¹ × 19¹

Step-3: Factors of 49380

List of positive integer factors of 49380 that divides 49380 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 823, 1646, 2469, 3292, 4115, 4938, 8230, 9876, 12345, 16460, 24690

Step-4: Factors of 49400

List of positive integer factors of 49400 that divides 49380 without a remainder.

1, 2, 4, 5, 8, 10, 13, 19, 20, 25, 26, 38, 40, 50, 52, 65, 76, 95, 100, 104, 130, 152, 190, 200, 247, 260, 325, 380, 475, 494, 520, 650, 760, 950, 988, 1235, 1300, 1900, 1976, 2470, 2600, 3800, 4940, 6175, 9880, 12350, 24700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49380 and 49400. The biggest common factor number is the GCF number.
So the greatest common factor 49380 and 49400 is 20.

Also check out the Least Common Multiple of 49380 and 49400