What is the Greatest Common Factor of 69750 and 69768?

Greatest common factor (GCF) of 69750 and 69768 is 18.

GCF(69750,69768) = 18

We will now calculate the prime factors of 69750 and 69768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69750 and 69768.

How to find the GCF of 69750 and 69768?

We will first find the prime factorization of 69750 and 69768. After we will calculate the factors of 69750 and 69768 and find the biggest common factor number .

Step-1: Prime Factorization of 69750

Prime factors of 69750 are 2, 3, 5, 31. Prime factorization of 69750 in exponential form is:

69750 = 2¹ × 3² × 5³ × 31¹

Step-2: Prime Factorization of 69768

Prime factors of 69768 are 2, 3, 17, 19. Prime factorization of 69768 in exponential form is:

69768 = 2³ × 3³ × 17¹ × 19¹

Step-3: Factors of 69750

List of positive integer factors of 69750 that divides 69750 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 31, 45, 50, 62, 75, 90, 93, 125, 150, 155, 186, 225, 250, 279, 310, 375, 450, 465, 558, 750, 775, 930, 1125, 1395, 1550, 2250, 2325, 2790, 3875, 4650, 6975, 7750, 11625, 13950, 23250, 34875

Step-4: Factors of 69768

List of positive integer factors of 69768 that divides 69750 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 19, 24, 27, 34, 36, 38, 51, 54, 57, 68, 72, 76, 102, 108, 114, 136, 152, 153, 171, 204, 216, 228, 306, 323, 342, 408, 456, 459, 513, 612, 646, 684, 918, 969, 1026, 1224, 1292, 1368, 1836, 1938, 2052, 2584, 2907, 3672, 3876, 4104, 5814, 7752, 8721, 11628, 17442, 23256, 34884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69750 and 69768. The biggest common factor number is the GCF number.
So the greatest common factor 69750 and 69768 is 18.

Also check out the Least Common Multiple of 69750 and 69768