What is the Greatest Common Factor of 38208 and 38220?

Greatest common factor (GCF) of 38208 and 38220 is 12.

GCF(38208,38220) = 12

We will now calculate the prime factors of 38208 and 38220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38208 and 38220.

How to find the GCF of 38208 and 38220?

We will first find the prime factorization of 38208 and 38220. After we will calculate the factors of 38208 and 38220 and find the biggest common factor number .

Step-1: Prime Factorization of 38208

Prime factors of 38208 are 2, 3, 199. Prime factorization of 38208 in exponential form is:

38208 = 2⁶ × 3¹ × 199¹

Step-2: Prime Factorization of 38220

Prime factors of 38220 are 2, 3, 5, 7, 13. Prime factorization of 38220 in exponential form is:

38220 = 2² × 3¹ × 5¹ × 7² × 13¹

Step-3: Factors of 38208

List of positive integer factors of 38208 that divides 38208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 199, 398, 597, 796, 1194, 1592, 2388, 3184, 4776, 6368, 9552, 12736, 19104

Step-4: Factors of 38220

List of positive integer factors of 38220 that divides 38208 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 49, 52, 60, 65, 70, 78, 84, 91, 98, 105, 130, 140, 147, 156, 182, 195, 196, 210, 245, 260, 273, 294, 364, 390, 420, 455, 490, 546, 588, 637, 735, 780, 910, 980, 1092, 1274, 1365, 1470, 1820, 1911, 2548, 2730, 2940, 3185, 3822, 5460, 6370, 7644, 9555, 12740, 19110

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38208 and 38220. The biggest common factor number is the GCF number.
So the greatest common factor 38208 and 38220 is 12.

Also check out the Least Common Multiple of 38208 and 38220