What is the Greatest Common Factor of 49200 and 49217?

Greatest common factor (GCF) of 49200 and 49217 is 1.

GCF(49200,49217) = 1

We will now calculate the prime factors of 49200 and 49217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49200 and 49217.

How to find the GCF of 49200 and 49217?

We will first find the prime factorization of 49200 and 49217. After we will calculate the factors of 49200 and 49217 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 49217

Prime factors of 49217 are 7, 79, 89. Prime factorization of 49217 in exponential form is:

49217 = 7¹ × 79¹ × 89¹

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 49217

List of positive integer factors of 49217 that divides 49200 without a remainder.

1, 7, 79, 89, 553, 623, 7031

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49200 and 49217. The biggest common factor number is the GCF number.
So the greatest common factor 49200 and 49217 is 1.

Also check out the Least Common Multiple of 49200 and 49217