What is the Greatest Common Factor of 37905 and 37914?

Greatest common factor (GCF) of 37905 and 37914 is 3.

GCF(37905,37914) = 3

We will now calculate the prime factors of 37905 and 37914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37905 and 37914.

How to find the GCF of 37905 and 37914?

We will first find the prime factorization of 37905 and 37914. After we will calculate the factors of 37905 and 37914 and find the biggest common factor number .

Step-1: Prime Factorization of 37905

Prime factors of 37905 are 3, 5, 7, 19. Prime factorization of 37905 in exponential form is:

37905 = 3¹ × 5¹ × 7¹ × 19²

Step-2: Prime Factorization of 37914

Prime factors of 37914 are 2, 3, 71, 89. Prime factorization of 37914 in exponential form is:

37914 = 2¹ × 3¹ × 71¹ × 89¹

Step-3: Factors of 37905

List of positive integer factors of 37905 that divides 37905 without a remainder.

1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 361, 399, 665, 1083, 1805, 1995, 2527, 5415, 7581, 12635

Step-4: Factors of 37914

List of positive integer factors of 37914 that divides 37905 without a remainder.

1, 2, 3, 6, 71, 89, 142, 178, 213, 267, 426, 534, 6319, 12638, 18957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37905 and 37914. The biggest common factor number is the GCF number.
So the greatest common factor 37905 and 37914 is 3.

Also check out the Least Common Multiple of 37905 and 37914