What is the Greatest Common Factor of 69300 and 69314?

Greatest common factor (GCF) of 69300 and 69314 is 14.

GCF(69300,69314) = 14

We will now calculate the prime factors of 69300 and 69314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69300 and 69314.

How to find the GCF of 69300 and 69314?

We will first find the prime factorization of 69300 and 69314. After we will calculate the factors of 69300 and 69314 and find the biggest common factor number .

Step-1: Prime Factorization of 69300

Prime factors of 69300 are 2, 3, 5, 7, 11. Prime factorization of 69300 in exponential form is:

69300 = 2² × 3² × 5² × 7¹ × 11¹

Step-2: Prime Factorization of 69314

Prime factors of 69314 are 2, 7, 4951. Prime factorization of 69314 in exponential form is:

69314 = 2¹ × 7¹ × 4951¹

Step-3: Factors of 69300

List of positive integer factors of 69300 that divides 69300 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 25, 28, 30, 33, 35, 36, 42, 44, 45, 50, 55, 60, 63, 66, 70, 75, 77, 84, 90, 99, 100, 105, 110, 126, 132, 140, 150, 154, 165, 175, 180, 198, 210, 220, 225, 231, 252, 275, 300, 308, 315, 330, 350, 385, 396, 420, 450, 462, 495, 525, 550, 630, 660, 693, 700, 770, 825, 900, 924, 990, 1050, 1100, 1155, 1260, 1386, 1540, 1575, 1650, 1925, 1980, 2100, 2310, 2475, 2772, 3150, 3300, 3465, 3850, 4620, 4950, 5775, 6300, 6930, 7700, 9900, 11550, 13860, 17325, 23100, 34650

Step-4: Factors of 69314

List of positive integer factors of 69314 that divides 69300 without a remainder.

1, 2, 7, 14, 4951, 9902, 34657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69300 and 69314. The biggest common factor number is the GCF number.
So the greatest common factor 69300 and 69314 is 14.

Also check out the Least Common Multiple of 69300 and 69314