What is the Greatest Common Factor of 1905 and 1925?

Greatest common factor (GCF) of 1905 and 1925 is 5.

GCF(1905,1925) = 5

We will now calculate the prime factors of 1905 and 1925, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1905 and 1925.

How to find the GCF of 1905 and 1925?

We will first find the prime factorization of 1905 and 1925. After we will calculate the factors of 1905 and 1925 and find the biggest common factor number .

Step-1: Prime Factorization of 1905

Prime factors of 1905 are 3, 5, 127. Prime factorization of 1905 in exponential form is:

1905 = 3¹ × 5¹ × 127¹

Step-2: Prime Factorization of 1925

Prime factors of 1925 are 5, 7, 11. Prime factorization of 1925 in exponential form is:

1925 = 5² × 7¹ × 11¹

Step-3: Factors of 1905

List of positive integer factors of 1905 that divides 1905 without a remainder.

1, 3, 5, 15, 127, 381, 635

Step-4: Factors of 1925

List of positive integer factors of 1925 that divides 1905 without a remainder.

1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1905 and 1925. The biggest common factor number is the GCF number.
So the greatest common factor 1905 and 1925 is 5.

Also check out the Least Common Multiple of 1905 and 1925