What is the Greatest Common Factor of 75104 and 75120?

Greatest common factor (GCF) of 75104 and 75120 is 16.

GCF(75104,75120) = 16

We will now calculate the prime factors of 75104 and 75120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75104 and 75120.

How to find the GCF of 75104 and 75120?

We will first find the prime factorization of 75104 and 75120. After we will calculate the factors of 75104 and 75120 and find the biggest common factor number .

Step-1: Prime Factorization of 75104

Prime factors of 75104 are 2, 2347. Prime factorization of 75104 in exponential form is:

75104 = 2⁵ × 2347¹

Step-2: 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-3: Factors of 75104

List of positive integer factors of 75104 that divides 75104 without a remainder.

1, 2, 4, 8, 16, 32, 2347, 4694, 9388, 18776, 37552

Step-4: Factors of 75120

List of positive integer factors of 75120 that divides 75104 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75104 and 75120. The biggest common factor number is the GCF number.
So the greatest common factor 75104 and 75120 is 16.

Also check out the Least Common Multiple of 75104 and 75120