What is the Greatest Common Factor of 49140 and 49154?

Greatest common factor (GCF) of 49140 and 49154 is 14.

GCF(49140,49154) = 14

We will now calculate the prime factors of 49140 and 49154, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49140 and 49154.

How to find the GCF of 49140 and 49154?

We will first find the prime factorization of 49140 and 49154. After we will calculate the factors of 49140 and 49154 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 49154

Prime factors of 49154 are 2, 7, 3511. Prime factorization of 49154 in exponential form is:

49154 = 2¹ × 7¹ × 3511¹

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 49154

List of positive integer factors of 49154 that divides 49140 without a remainder.

1, 2, 7, 14, 3511, 7022, 24577

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49140 and 49154. The biggest common factor number is the GCF number.
So the greatest common factor 49140 and 49154 is 14.

Also check out the Least Common Multiple of 49140 and 49154