What is the Greatest Common Factor of 82075 and 82080?

Greatest common factor (GCF) of 82075 and 82080 is 5.

GCF(82075,82080) = 5

We will now calculate the prime factors of 82075 and 82080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82075 and 82080.

How to find the GCF of 82075 and 82080?

We will first find the prime factorization of 82075 and 82080. After we will calculate the factors of 82075 and 82080 and find the biggest common factor number .

Step-1: Prime Factorization of 82075

Prime factors of 82075 are 5, 7, 67. Prime factorization of 82075 in exponential form is:

82075 = 5² × 7² × 67¹

Step-2: Prime Factorization of 82080

Prime factors of 82080 are 2, 3, 5, 19. Prime factorization of 82080 in exponential form is:

82080 = 2⁵ × 3³ × 5¹ × 19¹

Step-3: Factors of 82075

List of positive integer factors of 82075 that divides 82075 without a remainder.

1, 5, 7, 25, 35, 49, 67, 175, 245, 335, 469, 1225, 1675, 2345, 3283, 11725, 16415

Step-4: Factors of 82080

List of positive integer factors of 82080 that divides 82075 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 27, 30, 32, 36, 38, 40, 45, 48, 54, 57, 60, 72, 76, 80, 90, 95, 96, 108, 114, 120, 135, 144, 152, 160, 171, 180, 190, 216, 228, 240, 270, 285, 288, 304, 342, 360, 380, 432, 456, 480, 513, 540, 570, 608, 684, 720, 760, 855, 864, 912, 1026, 1080, 1140, 1368, 1440, 1520, 1710, 1824, 2052, 2160, 2280, 2565, 2736, 3040, 3420, 4104, 4320, 4560, 5130, 5472, 6840, 8208, 9120, 10260, 13680, 16416, 20520, 27360, 41040

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82075 and 82080. The biggest common factor number is the GCF number.
So the greatest common factor 82075 and 82080 is 5.

Also check out the Least Common Multiple of 82075 and 82080