What is the Greatest Common Factor of 61914 and 61920?

Greatest common factor (GCF) of 61914 and 61920 is 6.

GCF(61914,61920) = 6

We will now calculate the prime factors of 61914 and 61920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61914 and 61920.

How to find the GCF of 61914 and 61920?

We will first find the prime factorization of 61914 and 61920. After we will calculate the factors of 61914 and 61920 and find the biggest common factor number .

Step-1: Prime Factorization of 61914

Prime factors of 61914 are 2, 3, 17, 607. Prime factorization of 61914 in exponential form is:

61914 = 2¹ × 3¹ × 17¹ × 607¹

Step-2: Prime Factorization of 61920

Prime factors of 61920 are 2, 3, 5, 43. Prime factorization of 61920 in exponential form is:

61920 = 2⁵ × 3² × 5¹ × 43¹

Step-3: Factors of 61914

List of positive integer factors of 61914 that divides 61914 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 607, 1214, 1821, 3642, 10319, 20638, 30957

Step-4: Factors of 61920

List of positive integer factors of 61920 that divides 61914 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 43, 45, 48, 60, 72, 80, 86, 90, 96, 120, 129, 144, 160, 172, 180, 215, 240, 258, 288, 344, 360, 387, 430, 480, 516, 645, 688, 720, 774, 860, 1032, 1290, 1376, 1440, 1548, 1720, 1935, 2064, 2580, 3096, 3440, 3870, 4128, 5160, 6192, 6880, 7740, 10320, 12384, 15480, 20640, 30960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61914 and 61920. The biggest common factor number is the GCF number.
So the greatest common factor 61914 and 61920 is 6.

Also check out the Least Common Multiple of 61914 and 61920