What is the Greatest Common Factor of 19312 and 19320?

Greatest common factor (GCF) of 19312 and 19320 is 8.

GCF(19312,19320) = 8

We will now calculate the prime factors of 19312 and 19320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19312 and 19320.

How to find the GCF of 19312 and 19320?

We will first find the prime factorization of 19312 and 19320. After we will calculate the factors of 19312 and 19320 and find the biggest common factor number .

Step-1: Prime Factorization of 19312

Prime factors of 19312 are 2, 17, 71. Prime factorization of 19312 in exponential form is:

19312 = 2⁴ × 17¹ × 71¹

Step-2: Prime Factorization of 19320

Prime factors of 19320 are 2, 3, 5, 7, 23. Prime factorization of 19320 in exponential form is:

19320 = 2³ × 3¹ × 5¹ × 7¹ × 23¹

Step-3: Factors of 19312

List of positive integer factors of 19312 that divides 19312 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 71, 136, 142, 272, 284, 568, 1136, 1207, 2414, 4828, 9656

Step-4: Factors of 19320

List of positive integer factors of 19320 that divides 19312 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 23, 24, 28, 30, 35, 40, 42, 46, 56, 60, 69, 70, 84, 92, 105, 115, 120, 138, 140, 161, 168, 184, 210, 230, 276, 280, 322, 345, 420, 460, 483, 552, 644, 690, 805, 840, 920, 966, 1288, 1380, 1610, 1932, 2415, 2760, 3220, 3864, 4830, 6440, 9660

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19312 and 19320. The biggest common factor number is the GCF number.
So the greatest common factor 19312 and 19320 is 8.

Also check out the Least Common Multiple of 19312 and 19320