What is the Greatest Common Factor of 19375 and 19380?

Greatest common factor (GCF) of 19375 and 19380 is 5.

GCF(19375,19380) = 5

We will now calculate the prime factors of 19375 and 19380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19375 and 19380.

How to find the GCF of 19375 and 19380?

We will first find the prime factorization of 19375 and 19380. After we will calculate the factors of 19375 and 19380 and find the biggest common factor number .

Step-1: Prime Factorization of 19375

Prime factors of 19375 are 5, 31. Prime factorization of 19375 in exponential form is:

19375 = 5⁴ × 31¹

Step-2: Prime Factorization of 19380

Prime factors of 19380 are 2, 3, 5, 17, 19. Prime factorization of 19380 in exponential form is:

19380 = 2² × 3¹ × 5¹ × 17¹ × 19¹

Step-3: Factors of 19375

List of positive integer factors of 19375 that divides 19375 without a remainder.

1, 5, 25, 31, 125, 155, 625, 775, 3875

Step-4: Factors of 19380

List of positive integer factors of 19380 that divides 19375 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 19, 20, 30, 34, 38, 51, 57, 60, 68, 76, 85, 95, 102, 114, 170, 190, 204, 228, 255, 285, 323, 340, 380, 510, 570, 646, 969, 1020, 1140, 1292, 1615, 1938, 3230, 3876, 4845, 6460, 9690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19375 and 19380. The biggest common factor number is the GCF number.
So the greatest common factor 19375 and 19380 is 5.

Also check out the Least Common Multiple of 19375 and 19380