What is the Greatest Common Factor of 76125 and 76144?

Greatest common factor (GCF) of 76125 and 76144 is 1.

GCF(76125,76144) = 1

We will now calculate the prime factors of 76125 and 76144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76125 and 76144.

How to find the GCF of 76125 and 76144?

We will first find the prime factorization of 76125 and 76144. After we will calculate the factors of 76125 and 76144 and find the biggest common factor number .

Step-1: Prime Factorization of 76125

Prime factors of 76125 are 3, 5, 7, 29. Prime factorization of 76125 in exponential form is:

76125 = 3¹ × 5³ × 7¹ × 29¹

Step-2: Prime Factorization of 76144

Prime factors of 76144 are 2, 4759. Prime factorization of 76144 in exponential form is:

76144 = 2⁴ × 4759¹

Step-3: Factors of 76125

List of positive integer factors of 76125 that divides 76125 without a remainder.

1, 3, 5, 7, 15, 21, 25, 29, 35, 75, 87, 105, 125, 145, 175, 203, 375, 435, 525, 609, 725, 875, 1015, 2175, 2625, 3045, 3625, 5075, 10875, 15225, 25375

Step-4: Factors of 76144

List of positive integer factors of 76144 that divides 76125 without a remainder.

1, 2, 4, 8, 16, 4759, 9518, 19036, 38072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76125 and 76144. The biggest common factor number is the GCF number.
So the greatest common factor 76125 and 76144 is 1.

Also check out the Least Common Multiple of 76125 and 76144