What is the Greatest Common Factor of 75100 and 75120?

Greatest common factor (GCF) of 75100 and 75120 is 20.

GCF(75100,75120) = 20

We will now calculate the prime factors of 75100 and 75120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75100 and 75120.

How to find the GCF of 75100 and 75120?

We will first find the prime factorization of 75100 and 75120. After we will calculate the factors of 75100 and 75120 and find the biggest common factor number .

Step-1: Prime Factorization of 75100

Prime factors of 75100 are 2, 5, 751. Prime factorization of 75100 in exponential form is:

75100 = 2² × 5² × 751¹

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 75100

List of positive integer factors of 75100 that divides 75100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 751, 1502, 3004, 3755, 7510, 15020, 18775, 37550

Step-4: Factors of 75120

List of positive integer factors of 75120 that divides 75100 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 75100 and 75120. The biggest common factor number is the GCF number.
So the greatest common factor 75100 and 75120 is 20.

Also check out the Least Common Multiple of 75100 and 75120