What is the Greatest Common Factor of 69749 and 69768?

Greatest common factor (GCF) of 69749 and 69768 is 19.

GCF(69749,69768) = 19

We will now calculate the prime factors of 69749 and 69768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69749 and 69768.

How to find the GCF of 69749 and 69768?

We will first find the prime factorization of 69749 and 69768. After we will calculate the factors of 69749 and 69768 and find the biggest common factor number .

Step-1: Prime Factorization of 69749

Prime factors of 69749 are 19, 3671. Prime factorization of 69749 in exponential form is:

69749 = 19¹ × 3671¹

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 69749

List of positive integer factors of 69749 that divides 69749 without a remainder.

1, 19, 3671

Step-4: Factors of 69768

List of positive integer factors of 69768 that divides 69749 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 69749 and 69768. The biggest common factor number is the GCF number.
So the greatest common factor 69749 and 69768 is 19.

Also check out the Least Common Multiple of 69749 and 69768