What is the Greatest Common Factor of 75284 and 75296?

Greatest common factor (GCF) of 75284 and 75296 is 4.

GCF(75284,75296) = 4

We will now calculate the prime factors of 75284 and 75296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75284 and 75296.

How to find the GCF of 75284 and 75296?

We will first find the prime factorization of 75284 and 75296. After we will calculate the factors of 75284 and 75296 and find the biggest common factor number .

Step-1: Prime Factorization of 75284

Prime factors of 75284 are 2, 11, 29, 59. Prime factorization of 75284 in exponential form is:

75284 = 2² × 11¹ × 29¹ × 59¹

Step-2: Prime Factorization of 75296

Prime factors of 75296 are 2, 13, 181. Prime factorization of 75296 in exponential form is:

75296 = 2⁵ × 13¹ × 181¹

Step-3: Factors of 75284

List of positive integer factors of 75284 that divides 75284 without a remainder.

1, 2, 4, 11, 22, 29, 44, 58, 59, 116, 118, 236, 319, 638, 649, 1276, 1298, 1711, 2596, 3422, 6844, 18821, 37642

Step-4: Factors of 75296

List of positive integer factors of 75296 that divides 75284 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 181, 208, 362, 416, 724, 1448, 2353, 2896, 4706, 5792, 9412, 18824, 37648

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75284 and 75296. The biggest common factor number is the GCF number.
So the greatest common factor 75284 and 75296 is 4.

Also check out the Least Common Multiple of 75284 and 75296