What is the Greatest Common Factor of 69000 and 69014?

Greatest common factor (GCF) of 69000 and 69014 is 2.

GCF(69000,69014) = 2

We will now calculate the prime factors of 69000 and 69014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69000 and 69014.

How to find the GCF of 69000 and 69014?

We will first find the prime factorization of 69000 and 69014. After we will calculate the factors of 69000 and 69014 and find the biggest common factor number .

Step-1: Prime Factorization of 69000

Prime factors of 69000 are 2, 3, 5, 23. Prime factorization of 69000 in exponential form is:

69000 = 2³ × 3¹ × 5³ × 23¹

Step-2: Prime Factorization of 69014

Prime factors of 69014 are 2, 11, 3137. Prime factorization of 69014 in exponential form is:

69014 = 2¹ × 11¹ × 3137¹

Step-3: Factors of 69000

List of positive integer factors of 69000 that divides 69000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 25, 30, 40, 46, 50, 60, 69, 75, 92, 100, 115, 120, 125, 138, 150, 184, 200, 230, 250, 276, 300, 345, 375, 460, 500, 552, 575, 600, 690, 750, 920, 1000, 1150, 1380, 1500, 1725, 2300, 2760, 2875, 3000, 3450, 4600, 5750, 6900, 8625, 11500, 13800, 17250, 23000, 34500

Step-4: Factors of 69014

List of positive integer factors of 69014 that divides 69000 without a remainder.

1, 2, 11, 22, 3137, 6274, 34507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69000 and 69014. The biggest common factor number is the GCF number.
So the greatest common factor 69000 and 69014 is 2.

Also check out the Least Common Multiple of 69000 and 69014