What is the Greatest Common Factor of 49140 and 49160?

Greatest common factor (GCF) of 49140 and 49160 is 20.

GCF(49140,49160) = 20

We will now calculate the prime factors of 49140 and 49160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49140 and 49160.

How to find the GCF of 49140 and 49160?

We will first find the prime factorization of 49140 and 49160. After we will calculate the factors of 49140 and 49160 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 49160

Prime factors of 49160 are 2, 5, 1229. Prime factorization of 49160 in exponential form is:

49160 = 2³ × 5¹ × 1229¹

Step-3: Factors of 49140

List of positive integer factors of 49140 that divides 49140 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

Step-4: Factors of 49160

List of positive integer factors of 49160 that divides 49140 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 1229, 2458, 4916, 6145, 9832, 12290, 24580

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49140 and 49160. The biggest common factor number is the GCF number.
So the greatest common factor 49140 and 49160 is 20.

Also check out the Least Common Multiple of 49140 and 49160