What is the Greatest Common Factor of 99975 and 99980?

Greatest common factor (GCF) of 99975 and 99980 is 5.

GCF(99975,99980) = 5

We will now calculate the prime factors of 99975 and 99980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 99975 and 99980.

How to find the GCF of 99975 and 99980?

We will first find the prime factorization of 99975 and 99980. After we will calculate the factors of 99975 and 99980 and find the biggest common factor number .

Step-1: Prime Factorization of 99975

Prime factors of 99975 are 3, 5, 31, 43. Prime factorization of 99975 in exponential form is:

99975 = 3¹ × 5² × 31¹ × 43¹

Step-2: Prime Factorization of 99980

Prime factors of 99980 are 2, 5, 4999. Prime factorization of 99980 in exponential form is:

99980 = 2² × 5¹ × 4999¹

Step-3: Factors of 99975

List of positive integer factors of 99975 that divides 99975 without a remainder.

1, 3, 5, 15, 25, 31, 43, 75, 93, 129, 155, 215, 465, 645, 775, 1075, 1333, 2325, 3225, 3999, 6665, 19995, 33325

Step-4: Factors of 99980

List of positive integer factors of 99980 that divides 99975 without a remainder.

1, 2, 4, 5, 10, 20, 4999, 9998, 19996, 24995, 49990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 99975 and 99980. The biggest common factor number is the GCF number.
So the greatest common factor 99975 and 99980 is 5.

Also check out the Least Common Multiple of 99975 and 99980