What is the Greatest Common Factor of 49400 and 49408?

Greatest common factor (GCF) of 49400 and 49408 is 8.

GCF(49400,49408) = 8

We will now calculate the prime factors of 49400 and 49408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49400 and 49408.

How to find the GCF of 49400 and 49408?

We will first find the prime factorization of 49400 and 49408. After we will calculate the factors of 49400 and 49408 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 49408

Prime factors of 49408 are 2, 193. Prime factorization of 49408 in exponential form is:

49408 = 2⁸ × 193¹

Step-3: Factors of 49400

List of positive integer factors of 49400 that divides 49400 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

Step-4: Factors of 49408

List of positive integer factors of 49408 that divides 49400 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 193, 256, 386, 772, 1544, 3088, 6176, 12352, 24704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49400 and 49408. The biggest common factor number is the GCF number.
So the greatest common factor 49400 and 49408 is 8.

Also check out the Least Common Multiple of 49400 and 49408