What is the Greatest Common Factor of 52000 and 52008?

Greatest common factor (GCF) of 52000 and 52008 is 8.

GCF(52000,52008) = 8

We will now calculate the prime factors of 52000 and 52008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52000 and 52008.

How to find the GCF of 52000 and 52008?

We will first find the prime factorization of 52000 and 52008. After we will calculate the factors of 52000 and 52008 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 52008

Prime factors of 52008 are 2, 3, 11, 197. Prime factorization of 52008 in exponential form is:

52008 = 2³ × 3¹ × 11¹ × 197¹

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 52008

List of positive integer factors of 52008 that divides 52000 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 197, 264, 394, 591, 788, 1182, 1576, 2167, 2364, 4334, 4728, 6501, 8668, 13002, 17336, 26004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52000 and 52008. The biggest common factor number is the GCF number.
So the greatest common factor 52000 and 52008 is 8.

Also check out the Least Common Multiple of 52000 and 52008