What is the Greatest Common Factor of 17766 and 17784?

Greatest common factor (GCF) of 17766 and 17784 is 18.

GCF(17766,17784) = 18

We will now calculate the prime factors of 17766 and 17784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17766 and 17784.

How to find the GCF of 17766 and 17784?

We will first find the prime factorization of 17766 and 17784. After we will calculate the factors of 17766 and 17784 and find the biggest common factor number .

Step-1: Prime Factorization of 17766

Prime factors of 17766 are 2, 3, 7, 47. Prime factorization of 17766 in exponential form is:

17766 = 2¹ × 3³ × 7¹ × 47¹

Step-2: Prime Factorization of 17784

Prime factors of 17784 are 2, 3, 13, 19. Prime factorization of 17784 in exponential form is:

17784 = 2³ × 3² × 13¹ × 19¹

Step-3: Factors of 17766

List of positive integer factors of 17766 that divides 17766 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 47, 54, 63, 94, 126, 141, 189, 282, 329, 378, 423, 658, 846, 987, 1269, 1974, 2538, 2961, 5922, 8883

Step-4: Factors of 17784

List of positive integer factors of 17784 that divides 17766 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 19, 24, 26, 36, 38, 39, 52, 57, 72, 76, 78, 104, 114, 117, 152, 156, 171, 228, 234, 247, 312, 342, 456, 468, 494, 684, 741, 936, 988, 1368, 1482, 1976, 2223, 2964, 4446, 5928, 8892

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17766 and 17784. The biggest common factor number is the GCF number.
So the greatest common factor 17766 and 17784 is 18.

Also check out the Least Common Multiple of 17766 and 17784