What is the Greatest Common Factor of 67716 and 67734?

Greatest common factor (GCF) of 67716 and 67734 is 18.

GCF(67716,67734) = 18

We will now calculate the prime factors of 67716 and 67734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67716 and 67734.

How to find the GCF of 67716 and 67734?

We will first find the prime factorization of 67716 and 67734. After we will calculate the factors of 67716 and 67734 and find the biggest common factor number .

Step-1: Prime Factorization of 67716

Prime factors of 67716 are 2, 3, 11, 19. Prime factorization of 67716 in exponential form is:

67716 = 2² × 3⁴ × 11¹ × 19¹

Step-2: Prime Factorization of 67734

Prime factors of 67734 are 2, 3, 53, 71. Prime factorization of 67734 in exponential form is:

67734 = 2¹ × 3² × 53¹ × 71¹

Step-3: Factors of 67716

List of positive integer factors of 67716 that divides 67716 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 19, 22, 27, 33, 36, 38, 44, 54, 57, 66, 76, 81, 99, 108, 114, 132, 162, 171, 198, 209, 228, 297, 324, 342, 396, 418, 513, 594, 627, 684, 836, 891, 1026, 1188, 1254, 1539, 1782, 1881, 2052, 2508, 3078, 3564, 3762, 5643, 6156, 7524, 11286, 16929, 22572, 33858

Step-4: Factors of 67734

List of positive integer factors of 67734 that divides 67716 without a remainder.

1, 2, 3, 6, 9, 18, 53, 71, 106, 142, 159, 213, 318, 426, 477, 639, 954, 1278, 3763, 7526, 11289, 22578, 33867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67716 and 67734. The biggest common factor number is the GCF number.
So the greatest common factor 67716 and 67734 is 18.

Also check out the Least Common Multiple of 67716 and 67734