What is the Greatest Common Factor of 76680 and 76700?

Greatest common factor (GCF) of 76680 and 76700 is 20.

GCF(76680,76700) = 20

We will now calculate the prime factors of 76680 and 76700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76680 and 76700.

How to find the GCF of 76680 and 76700?

We will first find the prime factorization of 76680 and 76700. After we will calculate the factors of 76680 and 76700 and find the biggest common factor number .

Step-1: Prime Factorization of 76680

Prime factors of 76680 are 2, 3, 5, 71. Prime factorization of 76680 in exponential form is:

76680 = 2³ × 3³ × 5¹ × 71¹

Step-2: Prime Factorization of 76700

Prime factors of 76700 are 2, 5, 13, 59. Prime factorization of 76700 in exponential form is:

76700 = 2² × 5² × 13¹ × 59¹

Step-3: Factors of 76680

List of positive integer factors of 76680 that divides 76680 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 71, 72, 90, 108, 120, 135, 142, 180, 213, 216, 270, 284, 355, 360, 426, 540, 568, 639, 710, 852, 1065, 1080, 1278, 1420, 1704, 1917, 2130, 2556, 2840, 3195, 3834, 4260, 5112, 6390, 7668, 8520, 9585, 12780, 15336, 19170, 25560, 38340

Step-4: Factors of 76700

List of positive integer factors of 76700 that divides 76680 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 59, 65, 100, 118, 130, 236, 260, 295, 325, 590, 650, 767, 1180, 1300, 1475, 1534, 2950, 3068, 3835, 5900, 7670, 15340, 19175, 38350

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76680 and 76700. The biggest common factor number is the GCF number.
So the greatest common factor 76680 and 76700 is 20.

Also check out the Least Common Multiple of 76680 and 76700