What is the Greatest Common Factor of 52000 and 52016?

Greatest common factor (GCF) of 52000 and 52016 is 16.

GCF(52000,52016) = 16

We will now calculate the prime factors of 52000 and 52016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52000 and 52016.

How to find the GCF of 52000 and 52016?

We will first find the prime factorization of 52000 and 52016. After we will calculate the factors of 52000 and 52016 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 52016

Prime factors of 52016 are 2, 3251. Prime factorization of 52016 in exponential form is:

52016 = 2⁴ × 3251¹

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 52016

List of positive integer factors of 52016 that divides 52000 without a remainder.

1, 2, 4, 8, 16, 3251, 6502, 13004, 26008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52000 and 52016. The biggest common factor number is the GCF number.
So the greatest common factor 52000 and 52016 is 16.

Also check out the Least Common Multiple of 52000 and 52016