What is the Greatest Common Factor of 47124 and 47138?

Greatest common factor (GCF) of 47124 and 47138 is 14.

GCF(47124,47138) = 14

We will now calculate the prime factors of 47124 and 47138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47124 and 47138.

How to find the GCF of 47124 and 47138?

We will first find the prime factorization of 47124 and 47138. After we will calculate the factors of 47124 and 47138 and find the biggest common factor number .

Step-1: Prime Factorization of 47124

Prime factors of 47124 are 2, 3, 7, 11, 17. Prime factorization of 47124 in exponential form is:

47124 = 2² × 3² × 7¹ × 11¹ × 17¹

Step-2: Prime Factorization of 47138

Prime factors of 47138 are 2, 7, 13, 37. Prime factorization of 47138 in exponential form is:

47138 = 2¹ × 7² × 13¹ × 37¹

Step-3: Factors of 47124

List of positive integer factors of 47124 that divides 47124 without a remainder.

1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 17, 18, 21, 22, 28, 33, 34, 36, 42, 44, 51, 63, 66, 68, 77, 84, 99, 102, 119, 126, 132, 153, 154, 187, 198, 204, 231, 238, 252, 306, 308, 357, 374, 396, 462, 476, 561, 612, 693, 714, 748, 924, 1071, 1122, 1309, 1386, 1428, 1683, 2142, 2244, 2618, 2772, 3366, 3927, 4284, 5236, 6732, 7854, 11781, 15708, 23562

Step-4: Factors of 47138

List of positive integer factors of 47138 that divides 47124 without a remainder.

1, 2, 7, 13, 14, 26, 37, 49, 74, 91, 98, 182, 259, 481, 518, 637, 962, 1274, 1813, 3367, 3626, 6734, 23569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47124 and 47138. The biggest common factor number is the GCF number.
So the greatest common factor 47124 and 47138 is 14.

Also check out the Least Common Multiple of 47124 and 47138