What is the Greatest Common Factor of 72120 and 72128?

Greatest common factor (GCF) of 72120 and 72128 is 8.

GCF(72120,72128) = 8

We will now calculate the prime factors of 72120 and 72128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72120 and 72128.

How to find the GCF of 72120 and 72128?

We will first find the prime factorization of 72120 and 72128. After we will calculate the factors of 72120 and 72128 and find the biggest common factor number .

Step-1: Prime Factorization of 72120

Prime factors of 72120 are 2, 3, 5, 601. Prime factorization of 72120 in exponential form is:

72120 = 2³ × 3¹ × 5¹ × 601¹

Step-2: Prime Factorization of 72128

Prime factors of 72128 are 2, 7, 23. Prime factorization of 72128 in exponential form is:

72128 = 2⁶ × 7² × 23¹

Step-3: Factors of 72120

List of positive integer factors of 72120 that divides 72120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 601, 1202, 1803, 2404, 3005, 3606, 4808, 6010, 7212, 9015, 12020, 14424, 18030, 24040, 36060

Step-4: Factors of 72128

List of positive integer factors of 72128 that divides 72120 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 49, 56, 64, 92, 98, 112, 161, 184, 196, 224, 322, 368, 392, 448, 644, 736, 784, 1127, 1288, 1472, 1568, 2254, 2576, 3136, 4508, 5152, 9016, 10304, 18032, 36064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72120 and 72128. The biggest common factor number is the GCF number.
So the greatest common factor 72120 and 72128 is 8.

Also check out the Least Common Multiple of 72120 and 72128