What is the Greatest Common Factor of 77140 and 77154?

Greatest common factor (GCF) of 77140 and 77154 is 14.

GCF(77140,77154) = 14

We will now calculate the prime factors of 77140 and 77154, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77140 and 77154.

How to find the GCF of 77140 and 77154?

We will first find the prime factorization of 77140 and 77154. After we will calculate the factors of 77140 and 77154 and find the biggest common factor number .

Step-1: Prime Factorization of 77140

Prime factors of 77140 are 2, 5, 7, 19, 29. Prime factorization of 77140 in exponential form is:

77140 = 2² × 5¹ × 7¹ × 19¹ × 29¹

Step-2: Prime Factorization of 77154

Prime factors of 77154 are 2, 3, 7, 11, 167. Prime factorization of 77154 in exponential form is:

77154 = 2¹ × 3¹ × 7¹ × 11¹ × 167¹

Step-3: Factors of 77140

List of positive integer factors of 77140 that divides 77140 without a remainder.

1, 2, 4, 5, 7, 10, 14, 19, 20, 28, 29, 35, 38, 58, 70, 76, 95, 116, 133, 140, 145, 190, 203, 266, 290, 380, 406, 532, 551, 580, 665, 812, 1015, 1102, 1330, 2030, 2204, 2660, 2755, 3857, 4060, 5510, 7714, 11020, 15428, 19285, 38570

Step-4: Factors of 77154

List of positive integer factors of 77154 that divides 77140 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 167, 231, 334, 462, 501, 1002, 1169, 1837, 2338, 3507, 3674, 5511, 7014, 11022, 12859, 25718, 38577

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77140 and 77154. The biggest common factor number is the GCF number.
So the greatest common factor 77140 and 77154 is 14.

Also check out the Least Common Multiple of 77140 and 77154