What is the Greatest Common Factor of 57000 and 57008?

Greatest common factor (GCF) of 57000 and 57008 is 8.

GCF(57000,57008) = 8

We will now calculate the prime factors of 57000 and 57008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57000 and 57008.

How to find the GCF of 57000 and 57008?

We will first find the prime factorization of 57000 and 57008. After we will calculate the factors of 57000 and 57008 and find the biggest common factor number .

Step-1: Prime Factorization of 57000

Prime factors of 57000 are 2, 3, 5, 19. Prime factorization of 57000 in exponential form is:

57000 = 2³ × 3¹ × 5³ × 19¹

Step-2: Prime Factorization of 57008

Prime factors of 57008 are 2, 7, 509. Prime factorization of 57008 in exponential form is:

57008 = 2⁴ × 7¹ × 509¹

Step-3: Factors of 57000

List of positive integer factors of 57000 that divides 57000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 25, 30, 38, 40, 50, 57, 60, 75, 76, 95, 100, 114, 120, 125, 150, 152, 190, 200, 228, 250, 285, 300, 375, 380, 456, 475, 500, 570, 600, 750, 760, 950, 1000, 1140, 1425, 1500, 1900, 2280, 2375, 2850, 3000, 3800, 4750, 5700, 7125, 9500, 11400, 14250, 19000, 28500

Step-4: Factors of 57008

List of positive integer factors of 57008 that divides 57000 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 509, 1018, 2036, 3563, 4072, 7126, 8144, 14252, 28504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57000 and 57008. The biggest common factor number is the GCF number.
So the greatest common factor 57000 and 57008 is 8.

Also check out the Least Common Multiple of 57000 and 57008