What is the Greatest Common Factor of 19152 and 19170?

Greatest common factor (GCF) of 19152 and 19170 is 18.

GCF(19152,19170) = 18

We will now calculate the prime factors of 19152 and 19170, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19152 and 19170.

How to find the GCF of 19152 and 19170?

We will first find the prime factorization of 19152 and 19170. After we will calculate the factors of 19152 and 19170 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19170

Prime factors of 19170 are 2, 3, 5, 71. Prime factorization of 19170 in exponential form is:

19170 = 2¹ × 3³ × 5¹ × 71¹

Step-3: Factors of 19152

List of positive integer factors of 19152 that divides 19152 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

Step-4: Factors of 19170

List of positive integer factors of 19170 that divides 19152 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 71, 90, 135, 142, 213, 270, 355, 426, 639, 710, 1065, 1278, 1917, 2130, 3195, 3834, 6390, 9585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19152 and 19170. The biggest common factor number is the GCF number.
So the greatest common factor 19152 and 19170 is 18.

Also check out the Least Common Multiple of 19152 and 19170