What is the Greatest Common Factor of 69000 and 69008?

Greatest common factor (GCF) of 69000 and 69008 is 8.

GCF(69000,69008) = 8

We will now calculate the prime factors of 69000 and 69008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69000 and 69008.

How to find the GCF of 69000 and 69008?

We will first find the prime factorization of 69000 and 69008. After we will calculate the factors of 69000 and 69008 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 69008

Prime factors of 69008 are 2, 19, 227. Prime factorization of 69008 in exponential form is:

69008 = 2⁴ × 19¹ × 227¹

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 69008

List of positive integer factors of 69008 that divides 69000 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152, 227, 304, 454, 908, 1816, 3632, 4313, 8626, 17252, 34504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69000 and 69008. The biggest common factor number is the GCF number.
So the greatest common factor 69000 and 69008 is 8.

Also check out the Least Common Multiple of 69000 and 69008