What is the Greatest Common Factor of 75278 and 75292?

Greatest common factor (GCF) of 75278 and 75292 is 14.

GCF(75278,75292) = 14

We will now calculate the prime factors of 75278 and 75292, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75278 and 75292.

How to find the GCF of 75278 and 75292?

We will first find the prime factorization of 75278 and 75292. After we will calculate the factors of 75278 and 75292 and find the biggest common factor number .

Step-1: Prime Factorization of 75278

Prime factors of 75278 are 2, 7, 19, 283. Prime factorization of 75278 in exponential form is:

75278 = 2¹ × 7¹ × 19¹ × 283¹

Step-2: Prime Factorization of 75292

Prime factors of 75292 are 2, 7, 2689. Prime factorization of 75292 in exponential form is:

75292 = 2² × 7¹ × 2689¹

Step-3: Factors of 75278

List of positive integer factors of 75278 that divides 75278 without a remainder.

1, 2, 7, 14, 19, 38, 133, 266, 283, 566, 1981, 3962, 5377, 10754, 37639

Step-4: Factors of 75292

List of positive integer factors of 75292 that divides 75278 without a remainder.

1, 2, 4, 7, 14, 28, 2689, 5378, 10756, 18823, 37646

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75278 and 75292. The biggest common factor number is the GCF number.
So the greatest common factor 75278 and 75292 is 14.

Also check out the Least Common Multiple of 75278 and 75292