What is the Greatest Common Factor of 49125 and 49140?

Greatest common factor (GCF) of 49125 and 49140 is 15.

GCF(49125,49140) = 15

We will now calculate the prime factors of 49125 and 49140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49125 and 49140.

How to find the GCF of 49125 and 49140?

We will first find the prime factorization of 49125 and 49140. After we will calculate the factors of 49125 and 49140 and find the biggest common factor number .

Step-1: Prime Factorization of 49125

Prime factors of 49125 are 3, 5, 131. Prime factorization of 49125 in exponential form is:

49125 = 3¹ × 5³ × 131¹

Step-2: Prime Factorization of 49140

Prime factors of 49140 are 2, 3, 5, 7, 13. Prime factorization of 49140 in exponential form is:

49140 = 2² × 3³ × 5¹ × 7¹ × 13¹

Step-3: Factors of 49125

List of positive integer factors of 49125 that divides 49125 without a remainder.

1, 3, 5, 15, 25, 75, 125, 131, 375, 393, 655, 1965, 3275, 9825, 16375

Step-4: Factors of 49140

List of positive integer factors of 49140 that divides 49125 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 18, 20, 21, 26, 27, 28, 30, 35, 36, 39, 42, 45, 52, 54, 60, 63, 65, 70, 78, 84, 90, 91, 105, 108, 117, 126, 130, 135, 140, 156, 180, 182, 189, 195, 210, 234, 252, 260, 270, 273, 315, 351, 364, 378, 390, 420, 455, 468, 540, 546, 585, 630, 702, 756, 780, 819, 910, 945, 1092, 1170, 1260, 1365, 1404, 1638, 1755, 1820, 1890, 2340, 2457, 2730, 3276, 3510, 3780, 4095, 4914, 5460, 7020, 8190, 9828, 12285, 16380, 24570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49125 and 49140. The biggest common factor number is the GCF number.
So the greatest common factor 49125 and 49140 is 15.

Also check out the Least Common Multiple of 49125 and 49140