What is the Greatest Common Factor of 19264 and 19278?

Greatest common factor (GCF) of 19264 and 19278 is 14.

GCF(19264,19278) = 14

We will now calculate the prime factors of 19264 and 19278, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19264 and 19278.

How to find the GCF of 19264 and 19278?

We will first find the prime factorization of 19264 and 19278. After we will calculate the factors of 19264 and 19278 and find the biggest common factor number .

Step-1: Prime Factorization of 19264

Prime factors of 19264 are 2, 7, 43. Prime factorization of 19264 in exponential form is:

19264 = 2⁶ × 7¹ × 43¹

Step-2: Prime Factorization of 19278

Prime factors of 19278 are 2, 3, 7, 17. Prime factorization of 19278 in exponential form is:

19278 = 2¹ × 3⁴ × 7¹ × 17¹

Step-3: Factors of 19264

List of positive integer factors of 19264 that divides 19264 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 43, 56, 64, 86, 112, 172, 224, 301, 344, 448, 602, 688, 1204, 1376, 2408, 2752, 4816, 9632

Step-4: Factors of 19278

List of positive integer factors of 19278 that divides 19264 without a remainder.

1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 27, 34, 42, 51, 54, 63, 81, 102, 119, 126, 153, 162, 189, 238, 306, 357, 378, 459, 567, 714, 918, 1071, 1134, 1377, 2142, 2754, 3213, 6426, 9639

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19264 and 19278. The biggest common factor number is the GCF number.
So the greatest common factor 19264 and 19278 is 14.

Also check out the Least Common Multiple of 19264 and 19278