What is the Greatest Common Factor of 61296 and 61310?

Greatest common factor (GCF) of 61296 and 61310 is 2.

GCF(61296,61310) = 2

We will now calculate the prime factors of 61296 and 61310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61296 and 61310.

How to find the GCF of 61296 and 61310?

We will first find the prime factorization of 61296 and 61310. After we will calculate the factors of 61296 and 61310 and find the biggest common factor number .

Step-1: Prime Factorization of 61296

Prime factors of 61296 are 2, 3, 1277. Prime factorization of 61296 in exponential form is:

61296 = 2⁴ × 3¹ × 1277¹

Step-2: Prime Factorization of 61310

Prime factors of 61310 are 2, 5, 6131. Prime factorization of 61310 in exponential form is:

61310 = 2¹ × 5¹ × 6131¹

Step-3: Factors of 61296

List of positive integer factors of 61296 that divides 61296 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1277, 2554, 3831, 5108, 7662, 10216, 15324, 20432, 30648

Step-4: Factors of 61310

List of positive integer factors of 61310 that divides 61296 without a remainder.

1, 2, 5, 10, 6131, 12262, 30655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61296 and 61310. The biggest common factor number is the GCF number.
So the greatest common factor 61296 and 61310 is 2.

Also check out the Least Common Multiple of 61296 and 61310