What is the Greatest Common Factor of 71748 and 71760?

Greatest common factor (GCF) of 71748 and 71760 is 12.

GCF(71748,71760) = 12

We will now calculate the prime factors of 71748 and 71760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71748 and 71760.

How to find the GCF of 71748 and 71760?

We will first find the prime factorization of 71748 and 71760. After we will calculate the factors of 71748 and 71760 and find the biggest common factor number .

Step-1: Prime Factorization of 71748

Prime factors of 71748 are 2, 3, 1993. Prime factorization of 71748 in exponential form is:

71748 = 2² × 3² × 1993¹

Step-2: Prime Factorization of 71760

Prime factors of 71760 are 2, 3, 5, 13, 23. Prime factorization of 71760 in exponential form is:

71760 = 2⁴ × 3¹ × 5¹ × 13¹ × 23¹

Step-3: Factors of 71748

List of positive integer factors of 71748 that divides 71748 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1993, 3986, 5979, 7972, 11958, 17937, 23916, 35874

Step-4: Factors of 71760

List of positive integer factors of 71760 that divides 71748 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 23, 24, 26, 30, 39, 40, 46, 48, 52, 60, 65, 69, 78, 80, 92, 104, 115, 120, 130, 138, 156, 184, 195, 208, 230, 240, 260, 276, 299, 312, 345, 368, 390, 460, 520, 552, 598, 624, 690, 780, 897, 920, 1040, 1104, 1196, 1380, 1495, 1560, 1794, 1840, 2392, 2760, 2990, 3120, 3588, 4485, 4784, 5520, 5980, 7176, 8970, 11960, 14352, 17940, 23920, 35880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71748 and 71760. The biggest common factor number is the GCF number.
So the greatest common factor 71748 and 71760 is 12.

Also check out the Least Common Multiple of 71748 and 71760