What is the Greatest Common Factor of 80500 and 80514?

Greatest common factor (GCF) of 80500 and 80514 is 14.

GCF(80500,80514) = 14

We will now calculate the prime factors of 80500 and 80514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 80500 and 80514.

How to find the GCF of 80500 and 80514?

We will first find the prime factorization of 80500 and 80514. After we will calculate the factors of 80500 and 80514 and find the biggest common factor number .

Step-1: Prime Factorization of 80500

Prime factors of 80500 are 2, 5, 7, 23. Prime factorization of 80500 in exponential form is:

80500 = 2² × 5³ × 7¹ × 23¹

Step-2: Prime Factorization of 80514

Prime factors of 80514 are 2, 3, 7, 71. Prime factorization of 80514 in exponential form is:

80514 = 2¹ × 3⁴ × 7¹ × 71¹

Step-3: Factors of 80500

List of positive integer factors of 80500 that divides 80500 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 23, 25, 28, 35, 46, 50, 70, 92, 100, 115, 125, 140, 161, 175, 230, 250, 322, 350, 460, 500, 575, 644, 700, 805, 875, 1150, 1610, 1750, 2300, 2875, 3220, 3500, 4025, 5750, 8050, 11500, 16100, 20125, 40250

Step-4: Factors of 80514

List of positive integer factors of 80514 that divides 80500 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 71, 81, 126, 142, 162, 189, 213, 378, 426, 497, 567, 639, 994, 1134, 1278, 1491, 1917, 2982, 3834, 4473, 5751, 8946, 11502, 13419, 26838, 40257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 80500 and 80514. The biggest common factor number is the GCF number.
So the greatest common factor 80500 and 80514 is 14.

Also check out the Least Common Multiple of 80500 and 80514