What is the Greatest Common Factor of 83760 and 83780?

Greatest common factor (GCF) of 83760 and 83780 is 20.

GCF(83760,83780) = 20

We will now calculate the prime factors of 83760 and 83780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83760 and 83780.

How to find the GCF of 83760 and 83780?

We will first find the prime factorization of 83760 and 83780. After we will calculate the factors of 83760 and 83780 and find the biggest common factor number .

Step-1: Prime Factorization of 83760

Prime factors of 83760 are 2, 3, 5, 349. Prime factorization of 83760 in exponential form is:

83760 = 2⁴ × 3¹ × 5¹ × 349¹

Step-2: Prime Factorization of 83780

Prime factors of 83780 are 2, 5, 59, 71. Prime factorization of 83780 in exponential form is:

83780 = 2² × 5¹ × 59¹ × 71¹

Step-3: Factors of 83760

List of positive integer factors of 83760 that divides 83760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 349, 698, 1047, 1396, 1745, 2094, 2792, 3490, 4188, 5235, 5584, 6980, 8376, 10470, 13960, 16752, 20940, 27920, 41880

Step-4: Factors of 83780

List of positive integer factors of 83780 that divides 83760 without a remainder.

1, 2, 4, 5, 10, 20, 59, 71, 118, 142, 236, 284, 295, 355, 590, 710, 1180, 1420, 4189, 8378, 16756, 20945, 41890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83760 and 83780. The biggest common factor number is the GCF number.
So the greatest common factor 83760 and 83780 is 20.

Also check out the Least Common Multiple of 83760 and 83780