What is the Greatest Common Factor of 61950 and 61965?

Greatest common factor (GCF) of 61950 and 61965 is 15.

GCF(61950,61965) = 15

We will now calculate the prime factors of 61950 and 61965, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61950 and 61965.

How to find the GCF of 61950 and 61965?

We will first find the prime factorization of 61950 and 61965. After we will calculate the factors of 61950 and 61965 and find the biggest common factor number .

Step-1: Prime Factorization of 61950

Prime factors of 61950 are 2, 3, 5, 7, 59. Prime factorization of 61950 in exponential form is:

61950 = 2¹ × 3¹ × 5² × 7¹ × 59¹

Step-2: 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-3: Factors of 61950

List of positive integer factors of 61950 that divides 61950 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 59, 70, 75, 105, 118, 150, 175, 177, 210, 295, 350, 354, 413, 525, 590, 826, 885, 1050, 1239, 1475, 1770, 2065, 2478, 2950, 4130, 4425, 6195, 8850, 10325, 12390, 20650, 30975

Step-4: Factors of 61965

List of positive integer factors of 61965 that divides 61950 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61950 and 61965. The biggest common factor number is the GCF number.
So the greatest common factor 61950 and 61965 is 15.

Also check out the Least Common Multiple of 61950 and 61965