What is the Greatest Common Factor of 75120 and 75128?

Greatest common factor (GCF) of 75120 and 75128 is 8.

GCF(75120,75128) = 8

We will now calculate the prime factors of 75120 and 75128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75120 and 75128.

How to find the GCF of 75120 and 75128?

We will first find the prime factorization of 75120 and 75128. After we will calculate the factors of 75120 and 75128 and find the biggest common factor number .

Step-1: Prime Factorization of 75120

Prime factors of 75120 are 2, 3, 5, 313. Prime factorization of 75120 in exponential form is:

75120 = 2⁴ × 3¹ × 5¹ × 313¹

Step-2: Prime Factorization of 75128

Prime factors of 75128 are 2, 9391. Prime factorization of 75128 in exponential form is:

75128 = 2³ × 9391¹

Step-3: Factors of 75120

List of positive integer factors of 75120 that divides 75120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 313, 626, 939, 1252, 1565, 1878, 2504, 3130, 3756, 4695, 5008, 6260, 7512, 9390, 12520, 15024, 18780, 25040, 37560

Step-4: Factors of 75128

List of positive integer factors of 75128 that divides 75120 without a remainder.

1, 2, 4, 8, 9391, 18782, 37564

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75120 and 75128. The biggest common factor number is the GCF number.
So the greatest common factor 75120 and 75128 is 8.

Also check out the Least Common Multiple of 75120 and 75128