What is the Greatest Common Factor of 31104 and 31122?

Greatest common factor (GCF) of 31104 and 31122 is 18.

GCF(31104,31122) = 18

We will now calculate the prime factors of 31104 and 31122, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31104 and 31122.

How to find the GCF of 31104 and 31122?

We will first find the prime factorization of 31104 and 31122. After we will calculate the factors of 31104 and 31122 and find the biggest common factor number .

Step-1: Prime Factorization of 31104

Prime factors of 31104 are 2, 3. Prime factorization of 31104 in exponential form is:

31104 = 2⁷ × 3⁵

Step-2: Prime Factorization of 31122

Prime factors of 31122 are 2, 3, 7, 13, 19. Prime factorization of 31122 in exponential form is:

31122 = 2¹ × 3² × 7¹ × 13¹ × 19¹

Step-3: Factors of 31104

List of positive integer factors of 31104 that divides 31104 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 243, 288, 324, 384, 432, 486, 576, 648, 864, 972, 1152, 1296, 1728, 1944, 2592, 3456, 3888, 5184, 7776, 10368, 15552

Step-4: Factors of 31122

List of positive integer factors of 31122 that divides 31104 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 19, 21, 26, 38, 39, 42, 57, 63, 78, 91, 114, 117, 126, 133, 171, 182, 234, 247, 266, 273, 342, 399, 494, 546, 741, 798, 819, 1197, 1482, 1638, 1729, 2223, 2394, 3458, 4446, 5187, 10374, 15561

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31104 and 31122. The biggest common factor number is the GCF number.
So the greatest common factor 31104 and 31122 is 18.

Also check out the Least Common Multiple of 31104 and 31122