What is the Greatest Common Factor of 71940 and 71960?

Greatest common factor (GCF) of 71940 and 71960 is 20.

GCF(71940,71960) = 20

We will now calculate the prime factors of 71940 and 71960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71940 and 71960.

How to find the GCF of 71940 and 71960?

We will first find the prime factorization of 71940 and 71960. After we will calculate the factors of 71940 and 71960 and find the biggest common factor number .

Step-1: Prime Factorization of 71940

Prime factors of 71940 are 2, 3, 5, 11, 109. Prime factorization of 71940 in exponential form is:

71940 = 2² × 3¹ × 5¹ × 11¹ × 109¹

Step-2: Prime Factorization of 71960

Prime factors of 71960 are 2, 5, 7, 257. Prime factorization of 71960 in exponential form is:

71960 = 2³ × 5¹ × 7¹ × 257¹

Step-3: Factors of 71940

List of positive integer factors of 71940 that divides 71940 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 109, 110, 132, 165, 218, 220, 327, 330, 436, 545, 654, 660, 1090, 1199, 1308, 1635, 2180, 2398, 3270, 3597, 4796, 5995, 6540, 7194, 11990, 14388, 17985, 23980, 35970

Step-4: Factors of 71960

List of positive integer factors of 71960 that divides 71940 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 257, 280, 514, 1028, 1285, 1799, 2056, 2570, 3598, 5140, 7196, 8995, 10280, 14392, 17990, 35980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71940 and 71960. The biggest common factor number is the GCF number.
So the greatest common factor 71940 and 71960 is 20.

Also check out the Least Common Multiple of 71940 and 71960