What is the Greatest Common Factor of 49344 and 49350?

Greatest common factor (GCF) of 49344 and 49350 is 6.

GCF(49344,49350) = 6

We will now calculate the prime factors of 49344 and 49350, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49344 and 49350.

How to find the GCF of 49344 and 49350?

We will first find the prime factorization of 49344 and 49350. After we will calculate the factors of 49344 and 49350 and find the biggest common factor number .

Step-1: Prime Factorization of 49344

Prime factors of 49344 are 2, 3, 257. Prime factorization of 49344 in exponential form is:

49344 = 2⁶ × 3¹ × 257¹

Step-2: Prime Factorization of 49350

Prime factors of 49350 are 2, 3, 5, 7, 47. Prime factorization of 49350 in exponential form is:

49350 = 2¹ × 3¹ × 5² × 7¹ × 47¹

Step-3: Factors of 49344

List of positive integer factors of 49344 that divides 49344 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 257, 514, 771, 1028, 1542, 2056, 3084, 4112, 6168, 8224, 12336, 16448, 24672

Step-4: Factors of 49350

List of positive integer factors of 49350 that divides 49344 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 47, 50, 70, 75, 94, 105, 141, 150, 175, 210, 235, 282, 329, 350, 470, 525, 658, 705, 987, 1050, 1175, 1410, 1645, 1974, 2350, 3290, 3525, 4935, 7050, 8225, 9870, 16450, 24675

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49344 and 49350. The biggest common factor number is the GCF number.
So the greatest common factor 49344 and 49350 is 6.

Also check out the Least Common Multiple of 49344 and 49350