What is the Greatest Common Factor of 48289 and 48300?

Greatest common factor (GCF) of 48289 and 48300 is 1.

GCF(48289,48300) = 1

We will now calculate the prime factors of 48289 and 48300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48289 and 48300.

How to find the GCF of 48289 and 48300?

We will first find the prime factorization of 48289 and 48300. After we will calculate the factors of 48289 and 48300 and find the biggest common factor number .

Step-1: Prime Factorization of 48289

Prime factors of 48289 are 43, 1123. Prime factorization of 48289 in exponential form is:

48289 = 43¹ × 1123¹

Step-2: Prime Factorization of 48300

Prime factors of 48300 are 2, 3, 5, 7, 23. Prime factorization of 48300 in exponential form is:

48300 = 2² × 3¹ × 5² × 7¹ × 23¹

Step-3: Factors of 48289

List of positive integer factors of 48289 that divides 48289 without a remainder.

1, 43, 1123

Step-4: Factors of 48300

List of positive integer factors of 48300 that divides 48289 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 23, 25, 28, 30, 35, 42, 46, 50, 60, 69, 70, 75, 84, 92, 100, 105, 115, 138, 140, 150, 161, 175, 210, 230, 276, 300, 322, 345, 350, 420, 460, 483, 525, 575, 644, 690, 700, 805, 966, 1050, 1150, 1380, 1610, 1725, 1932, 2100, 2300, 2415, 3220, 3450, 4025, 4830, 6900, 8050, 9660, 12075, 16100, 24150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48289 and 48300. The biggest common factor number is the GCF number.
So the greatest common factor 48289 and 48300 is 1.

Also check out the Least Common Multiple of 48289 and 48300