What is the Greatest Common Factor of 75408 and 75420?

Greatest common factor (GCF) of 75408 and 75420 is 12.

GCF(75408,75420) = 12

We will now calculate the prime factors of 75408 and 75420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75408 and 75420.

How to find the GCF of 75408 and 75420?

We will first find the prime factorization of 75408 and 75420. After we will calculate the factors of 75408 and 75420 and find the biggest common factor number .

Step-1: Prime Factorization of 75408

Prime factors of 75408 are 2, 3, 1571. Prime factorization of 75408 in exponential form is:

75408 = 2⁴ × 3¹ × 1571¹

Step-2: Prime Factorization of 75420

Prime factors of 75420 are 2, 3, 5, 419. Prime factorization of 75420 in exponential form is:

75420 = 2² × 3² × 5¹ × 419¹

Step-3: Factors of 75408

List of positive integer factors of 75408 that divides 75408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1571, 3142, 4713, 6284, 9426, 12568, 18852, 25136, 37704

Step-4: Factors of 75420

List of positive integer factors of 75420 that divides 75408 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 419, 838, 1257, 1676, 2095, 2514, 3771, 4190, 5028, 6285, 7542, 8380, 12570, 15084, 18855, 25140, 37710

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75408 and 75420. The biggest common factor number is the GCF number.
So the greatest common factor 75408 and 75420 is 12.

Also check out the Least Common Multiple of 75408 and 75420