What is the Greatest Common Factor of 49200 and 49209?

Greatest common factor (GCF) of 49200 and 49209 is 3.

GCF(49200,49209) = 3

We will now calculate the prime factors of 49200 and 49209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49200 and 49209.

How to find the GCF of 49200 and 49209?

We will first find the prime factorization of 49200 and 49209. After we will calculate the factors of 49200 and 49209 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 49209

Prime factors of 49209 are 3, 47, 349. Prime factorization of 49209 in exponential form is:

49209 = 3¹ × 47¹ × 349¹

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 49209

List of positive integer factors of 49209 that divides 49200 without a remainder.

1, 3, 47, 141, 349, 1047, 16403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49200 and 49209. The biggest common factor number is the GCF number.
So the greatest common factor 49200 and 49209 is 3.

Also check out the Least Common Multiple of 49200 and 49209