What is the Greatest Common Factor of 71940 and 71952?

Greatest common factor (GCF) of 71940 and 71952 is 12.

GCF(71940,71952) = 12

We will now calculate the prime factors of 71940 and 71952, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71940 and 71952.

How to find the GCF of 71940 and 71952?

We will first find the prime factorization of 71940 and 71952. After we will calculate the factors of 71940 and 71952 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 71952

Prime factors of 71952 are 2, 3, 1499. Prime factorization of 71952 in exponential form is:

71952 = 2⁴ × 3¹ × 1499¹

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 71952

List of positive integer factors of 71952 that divides 71940 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1499, 2998, 4497, 5996, 8994, 11992, 17988, 23984, 35976

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71940 and 71952. The biggest common factor number is the GCF number.
So the greatest common factor 71940 and 71952 is 12.

Also check out the Least Common Multiple of 71940 and 71952