What is the Greatest Common Factor of 75068 and 75072?

Greatest common factor (GCF) of 75068 and 75072 is 4.

GCF(75068,75072) = 4

We will now calculate the prime factors of 75068 and 75072, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75068 and 75072.

How to find the GCF of 75068 and 75072?

We will first find the prime factorization of 75068 and 75072. After we will calculate the factors of 75068 and 75072 and find the biggest common factor number .

Step-1: Prime Factorization of 75068

Prime factors of 75068 are 2, 7, 383. Prime factorization of 75068 in exponential form is:

75068 = 2² × 7² × 383¹

Step-2: Prime Factorization of 75072

Prime factors of 75072 are 2, 3, 17, 23. Prime factorization of 75072 in exponential form is:

75072 = 2⁶ × 3¹ × 17¹ × 23¹

Step-3: Factors of 75068

List of positive integer factors of 75068 that divides 75068 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196, 383, 766, 1532, 2681, 5362, 10724, 18767, 37534

Step-4: Factors of 75072

List of positive integer factors of 75072 that divides 75068 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 23, 24, 32, 34, 46, 48, 51, 64, 68, 69, 92, 96, 102, 136, 138, 184, 192, 204, 272, 276, 368, 391, 408, 544, 552, 736, 782, 816, 1088, 1104, 1173, 1472, 1564, 1632, 2208, 2346, 3128, 3264, 4416, 4692, 6256, 9384, 12512, 18768, 25024, 37536

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75068 and 75072. The biggest common factor number is the GCF number.
So the greatest common factor 75068 and 75072 is 4.

Also check out the Least Common Multiple of 75068 and 75072