What is the Greatest Common Factor of 49200 and 49220?

Greatest common factor (GCF) of 49200 and 49220 is 20.

GCF(49200,49220) = 20

We will now calculate the prime factors of 49200 and 49220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49200 and 49220.

How to find the GCF of 49200 and 49220?

We will first find the prime factorization of 49200 and 49220. After we will calculate the factors of 49200 and 49220 and find the biggest common factor number .

Step-1: Prime Factorization of 49200

Prime factors of 49200 are 2, 3, 5, 41. Prime factorization of 49200 in exponential form is:

49200 = 2⁴ × 3¹ × 5² × 41¹

Step-2: Prime Factorization of 49220

Prime factors of 49220 are 2, 5, 23, 107. Prime factorization of 49220 in exponential form is:

49220 = 2² × 5¹ × 23¹ × 107¹

Step-3: Factors of 49200

List of positive integer factors of 49200 that divides 49200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 41, 48, 50, 60, 75, 80, 82, 100, 120, 123, 150, 164, 200, 205, 240, 246, 300, 328, 400, 410, 492, 600, 615, 656, 820, 984, 1025, 1200, 1230, 1640, 1968, 2050, 2460, 3075, 3280, 4100, 4920, 6150, 8200, 9840, 12300, 16400, 24600

Step-4: Factors of 49220

List of positive integer factors of 49220 that divides 49200 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 107, 115, 214, 230, 428, 460, 535, 1070, 2140, 2461, 4922, 9844, 12305, 24610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49200 and 49220. The biggest common factor number is the GCF number.
So the greatest common factor 49200 and 49220 is 20.

Also check out the Least Common Multiple of 49200 and 49220