What is the Greatest Common Factor of 65904 and 65919?

Greatest common factor (GCF) of 65904 and 65919 is 3.

GCF(65904,65919) = 3

We will now calculate the prime factors of 65904 and 65919, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65904 and 65919.

How to find the GCF of 65904 and 65919?

We will first find the prime factorization of 65904 and 65919. After we will calculate the factors of 65904 and 65919 and find the biggest common factor number .

Step-1: Prime Factorization of 65904

Prime factors of 65904 are 2, 3, 1373. Prime factorization of 65904 in exponential form is:

65904 = 2⁴ × 3¹ × 1373¹

Step-2: Prime Factorization of 65919

Prime factors of 65919 are 3, 7, 43, 73. Prime factorization of 65919 in exponential form is:

65919 = 3¹ × 7¹ × 43¹ × 73¹

Step-3: Factors of 65904

List of positive integer factors of 65904 that divides 65904 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1373, 2746, 4119, 5492, 8238, 10984, 16476, 21968, 32952

Step-4: Factors of 65919

List of positive integer factors of 65919 that divides 65904 without a remainder.

1, 3, 7, 21, 43, 73, 129, 219, 301, 511, 903, 1533, 3139, 9417, 21973

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65904 and 65919. The biggest common factor number is the GCF number.
So the greatest common factor 65904 and 65919 is 3.

Also check out the Least Common Multiple of 65904 and 65919