What is the Greatest Common Factor of 71760 and 71776?

Greatest common factor (GCF) of 71760 and 71776 is 16.

GCF(71760,71776) = 16

We will now calculate the prime factors of 71760 and 71776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71760 and 71776.

How to find the GCF of 71760 and 71776?

We will first find the prime factorization of 71760 and 71776. After we will calculate the factors of 71760 and 71776 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 71776

Prime factors of 71776 are 2, 2243. Prime factorization of 71776 in exponential form is:

71776 = 2⁵ × 2243¹

Step-3: Factors of 71760

List of positive integer factors of 71760 that divides 71760 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

Step-4: Factors of 71776

List of positive integer factors of 71776 that divides 71760 without a remainder.

1, 2, 4, 8, 16, 32, 2243, 4486, 8972, 17944, 35888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71760 and 71776. The biggest common factor number is the GCF number.
So the greatest common factor 71760 and 71776 is 16.

Also check out the Least Common Multiple of 71760 and 71776