What is the Greatest Common Factor of 17776 and 17784?

Greatest common factor (GCF) of 17776 and 17784 is 8.

GCF(17776,17784) = 8

We will now calculate the prime factors of 17776 and 17784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17776 and 17784.

How to find the GCF of 17776 and 17784?

We will first find the prime factorization of 17776 and 17784. After we will calculate the factors of 17776 and 17784 and find the biggest common factor number .

Step-1: Prime Factorization of 17776

Prime factors of 17776 are 2, 11, 101. Prime factorization of 17776 in exponential form is:

17776 = 2⁴ × 11¹ × 101¹

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 17776

List of positive integer factors of 17776 that divides 17776 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 101, 176, 202, 404, 808, 1111, 1616, 2222, 4444, 8888

Step-4: Factors of 17784

List of positive integer factors of 17784 that divides 17776 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 17776 and 17784. The biggest common factor number is the GCF number.
So the greatest common factor 17776 and 17784 is 8.

Also check out the Least Common Multiple of 17776 and 17784