What is the Greatest Common Factor of 61965 and 61974?

Greatest common factor (GCF) of 61965 and 61974 is 9.

GCF(61965,61974) = 9

We will now calculate the prime factors of 61965 and 61974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61965 and 61974.

How to find the GCF of 61965 and 61974?

We will first find the prime factorization of 61965 and 61974. After we will calculate the factors of 61965 and 61974 and find the biggest common factor number .

Step-1: Prime Factorization of 61965

Prime factors of 61965 are 3, 5, 17. Prime factorization of 61965 in exponential form is:

61965 = 3⁶ × 5¹ × 17¹

Step-2: 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-3: Factors of 61965

List of positive integer factors of 61965 that divides 61965 without a remainder.

1, 3, 5, 9, 15, 17, 27, 45, 51, 81, 85, 135, 153, 243, 255, 405, 459, 729, 765, 1215, 1377, 2295, 3645, 4131, 6885, 12393, 20655

Step-4: Factors of 61974

List of positive integer factors of 61974 that divides 61965 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61965 and 61974. The biggest common factor number is the GCF number.
So the greatest common factor 61965 and 61974 is 9.

Also check out the Least Common Multiple of 61965 and 61974