What is the Greatest Common Factor of 77686 and 77700?

Greatest common factor (GCF) of 77686 and 77700 is 14.

GCF(77686,77700) = 14

We will now calculate the prime factors of 77686 and 77700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77686 and 77700.

How to find the GCF of 77686 and 77700?

We will first find the prime factorization of 77686 and 77700. After we will calculate the factors of 77686 and 77700 and find the biggest common factor number .

Step-1: Prime Factorization of 77686

Prime factors of 77686 are 2, 7, 31, 179. Prime factorization of 77686 in exponential form is:

77686 = 2¹ × 7¹ × 31¹ × 179¹

Step-2: Prime Factorization of 77700

Prime factors of 77700 are 2, 3, 5, 7, 37. Prime factorization of 77700 in exponential form is:

77700 = 2² × 3¹ × 5² × 7¹ × 37¹

Step-3: Factors of 77686

List of positive integer factors of 77686 that divides 77686 without a remainder.

1, 2, 7, 14, 31, 62, 179, 217, 358, 434, 1253, 2506, 5549, 11098, 38843

Step-4: Factors of 77700

List of positive integer factors of 77700 that divides 77686 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 37, 42, 50, 60, 70, 74, 75, 84, 100, 105, 111, 140, 148, 150, 175, 185, 210, 222, 259, 300, 350, 370, 420, 444, 518, 525, 555, 700, 740, 777, 925, 1036, 1050, 1110, 1295, 1554, 1850, 2100, 2220, 2590, 2775, 3108, 3700, 3885, 5180, 5550, 6475, 7770, 11100, 12950, 15540, 19425, 25900, 38850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77686 and 77700. The biggest common factor number is the GCF number.
So the greatest common factor 77686 and 77700 is 14.

Also check out the Least Common Multiple of 77686 and 77700