What is the Greatest Common Factor of 61974 and 61989?

Greatest common factor (GCF) of 61974 and 61989 is 3.

GCF(61974,61989) = 3

We will now calculate the prime factors of 61974 and 61989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61974 and 61989.

How to find the GCF of 61974 and 61989?

We will first find the prime factorization of 61974 and 61989. After we will calculate the factors of 61974 and 61989 and find the biggest common factor number .

Step-1: Prime Factorization of 61974

Prime factors of 61974 are 2, 3, 11, 313. Prime factorization of 61974 in exponential form is:

61974 = 2¹ × 3² × 11¹ × 313¹

Step-2: Prime Factorization of 61989

Prime factors of 61989 are 3, 20663. Prime factorization of 61989 in exponential form is:

61989 = 3¹ × 20663¹

Step-3: Factors of 61974

List of positive integer factors of 61974 that divides 61974 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198, 313, 626, 939, 1878, 2817, 3443, 5634, 6886, 10329, 20658, 30987

Step-4: Factors of 61989

List of positive integer factors of 61989 that divides 61974 without a remainder.

1, 3, 20663

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61974 and 61989. The biggest common factor number is the GCF number.
So the greatest common factor 61974 and 61989 is 3.

Also check out the Least Common Multiple of 61974 and 61989