What is the Greatest Common Factor of 68992 and 69000?

Greatest common factor (GCF) of 68992 and 69000 is 8.

GCF(68992,69000) = 8

We will now calculate the prime factors of 68992 and 69000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68992 and 69000.

How to find the GCF of 68992 and 69000?

We will first find the prime factorization of 68992 and 69000. After we will calculate the factors of 68992 and 69000 and find the biggest common factor number .

Step-1: Prime Factorization of 68992

Prime factors of 68992 are 2, 7, 11. Prime factorization of 68992 in exponential form is:

68992 = 2⁷ × 7² × 11¹

Step-2: 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-3: Factors of 68992

List of positive integer factors of 68992 that divides 68992 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 49, 56, 64, 77, 88, 98, 112, 128, 154, 176, 196, 224, 308, 352, 392, 448, 539, 616, 704, 784, 896, 1078, 1232, 1408, 1568, 2156, 2464, 3136, 4312, 4928, 6272, 8624, 9856, 17248, 34496

Step-4: Factors of 69000

List of positive integer factors of 69000 that divides 68992 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68992 and 69000. The biggest common factor number is the GCF number.
So the greatest common factor 68992 and 69000 is 8.

Also check out the Least Common Multiple of 68992 and 69000