What is the Greatest Common Factor of 69594 and 69600?

Greatest common factor (GCF) of 69594 and 69600 is 6.

GCF(69594,69600) = 6

We will now calculate the prime factors of 69594 and 69600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69594 and 69600.

How to find the GCF of 69594 and 69600?

We will first find the prime factorization of 69594 and 69600. After we will calculate the factors of 69594 and 69600 and find the biggest common factor number .

Step-1: Prime Factorization of 69594

Prime factors of 69594 are 2, 3, 7, 1657. Prime factorization of 69594 in exponential form is:

69594 = 2¹ × 3¹ × 7¹ × 1657¹

Step-2: Prime Factorization of 69600

Prime factors of 69600 are 2, 3, 5, 29. Prime factorization of 69600 in exponential form is:

69600 = 2⁵ × 3¹ × 5² × 29¹

Step-3: Factors of 69594

List of positive integer factors of 69594 that divides 69594 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1657, 3314, 4971, 9942, 11599, 23198, 34797

Step-4: Factors of 69600

List of positive integer factors of 69600 that divides 69594 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 29, 30, 32, 40, 48, 50, 58, 60, 75, 80, 87, 96, 100, 116, 120, 145, 150, 160, 174, 200, 232, 240, 290, 300, 348, 400, 435, 464, 480, 580, 600, 696, 725, 800, 870, 928, 1160, 1200, 1392, 1450, 1740, 2175, 2320, 2400, 2784, 2900, 3480, 4350, 4640, 5800, 6960, 8700, 11600, 13920, 17400, 23200, 34800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69594 and 69600. The biggest common factor number is the GCF number.
So the greatest common factor 69594 and 69600 is 6.

Also check out the Least Common Multiple of 69594 and 69600