What is the Greatest Common Factor of 52000 and 52014?

Greatest common factor (GCF) of 52000 and 52014 is 2.

GCF(52000,52014) = 2

We will now calculate the prime factors of 52000 and 52014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52000 and 52014.

How to find the GCF of 52000 and 52014?

We will first find the prime factorization of 52000 and 52014. After we will calculate the factors of 52000 and 52014 and find the biggest common factor number .

Step-1: Prime Factorization of 52000

Prime factors of 52000 are 2, 5, 13. Prime factorization of 52000 in exponential form is:

52000 = 2⁵ × 5³ × 13¹

Step-2: Prime Factorization of 52014

Prime factors of 52014 are 2, 3, 8669. Prime factorization of 52014 in exponential form is:

52014 = 2¹ × 3¹ × 8669¹

Step-3: Factors of 52000

List of positive integer factors of 52000 that divides 52000 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 65, 80, 100, 104, 125, 130, 160, 200, 208, 250, 260, 325, 400, 416, 500, 520, 650, 800, 1000, 1040, 1300, 1625, 2000, 2080, 2600, 3250, 4000, 5200, 6500, 10400, 13000, 26000

Step-4: Factors of 52014

List of positive integer factors of 52014 that divides 52000 without a remainder.

1, 2, 3, 6, 8669, 17338, 26007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52000 and 52014. The biggest common factor number is the GCF number.
So the greatest common factor 52000 and 52014 is 2.

Also check out the Least Common Multiple of 52000 and 52014