What is the Greatest Common Factor of 77680 and 77700?

Greatest common factor (GCF) of 77680 and 77700 is 20.

GCF(77680,77700) = 20

We will now calculate the prime factors of 77680 and 77700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77680 and 77700.

How to find the GCF of 77680 and 77700?

We will first find the prime factorization of 77680 and 77700. After we will calculate the factors of 77680 and 77700 and find the biggest common factor number .

Step-1: Prime Factorization of 77680

Prime factors of 77680 are 2, 5, 971. Prime factorization of 77680 in exponential form is:

77680 = 2⁴ × 5¹ × 971¹

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 77680

List of positive integer factors of 77680 that divides 77680 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 971, 1942, 3884, 4855, 7768, 9710, 15536, 19420, 38840

Step-4: Factors of 77700

List of positive integer factors of 77700 that divides 77680 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 77680 and 77700. The biggest common factor number is the GCF number.
So the greatest common factor 77680 and 77700 is 20.

Also check out the Least Common Multiple of 77680 and 77700