What is the Greatest Common Factor of 19138 and 19152?

Greatest common factor (GCF) of 19138 and 19152 is 14.

GCF(19138,19152) = 14

We will now calculate the prime factors of 19138 and 19152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19138 and 19152.

How to find the GCF of 19138 and 19152?

We will first find the prime factorization of 19138 and 19152. After we will calculate the factors of 19138 and 19152 and find the biggest common factor number .

Step-1: Prime Factorization of 19138

Prime factors of 19138 are 2, 7, 1367. Prime factorization of 19138 in exponential form is:

19138 = 2¹ × 7¹ × 1367¹

Step-2: Prime Factorization of 19152

Prime factors of 19152 are 2, 3, 7, 19. Prime factorization of 19152 in exponential form is:

19152 = 2⁴ × 3² × 7¹ × 19¹

Step-3: Factors of 19138

List of positive integer factors of 19138 that divides 19138 without a remainder.

1, 2, 7, 14, 1367, 2734, 9569

Step-4: Factors of 19152

List of positive integer factors of 19152 that divides 19138 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 28, 36, 38, 42, 48, 56, 57, 63, 72, 76, 84, 112, 114, 126, 133, 144, 152, 168, 171, 228, 252, 266, 304, 336, 342, 399, 456, 504, 532, 684, 798, 912, 1008, 1064, 1197, 1368, 1596, 2128, 2394, 2736, 3192, 4788, 6384, 9576

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19138 and 19152. The biggest common factor number is the GCF number.
So the greatest common factor 19138 and 19152 is 14.

Also check out the Least Common Multiple of 19138 and 19152