What is the Greatest Common Factor of 75120 and 75132?

Greatest common factor (GCF) of 75120 and 75132 is 12.

GCF(75120,75132) = 12

We will now calculate the prime factors of 75120 and 75132, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75120 and 75132.

How to find the GCF of 75120 and 75132?

We will first find the prime factorization of 75120 and 75132. After we will calculate the factors of 75120 and 75132 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 75132

Prime factors of 75132 are 2, 3, 2087. Prime factorization of 75132 in exponential form is:

75132 = 2² × 3² × 2087¹

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 75132

List of positive integer factors of 75132 that divides 75120 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2087, 4174, 6261, 8348, 12522, 18783, 25044, 37566

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75120 and 75132. The biggest common factor number is the GCF number.
So the greatest common factor 75120 and 75132 is 12.

Also check out the Least Common Multiple of 75120 and 75132