What is the Greatest Common Factor of 75628 and 75632?

Greatest common factor (GCF) of 75628 and 75632 is 4.

GCF(75628,75632) = 4

We will now calculate the prime factors of 75628 and 75632, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75628 and 75632.

How to find the GCF of 75628 and 75632?

We will first find the prime factorization of 75628 and 75632. After we will calculate the factors of 75628 and 75632 and find the biggest common factor number .

Step-1: Prime Factorization of 75628

Prime factors of 75628 are 2, 7, 37, 73. Prime factorization of 75628 in exponential form is:

75628 = 2² × 7¹ × 37¹ × 73¹

Step-2: Prime Factorization of 75632

Prime factors of 75632 are 2, 29, 163. Prime factorization of 75632 in exponential form is:

75632 = 2⁴ × 29¹ × 163¹

Step-3: Factors of 75628

List of positive integer factors of 75628 that divides 75628 without a remainder.

1, 2, 4, 7, 14, 28, 37, 73, 74, 146, 148, 259, 292, 511, 518, 1022, 1036, 2044, 2701, 5402, 10804, 18907, 37814

Step-4: Factors of 75632

List of positive integer factors of 75632 that divides 75628 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 163, 232, 326, 464, 652, 1304, 2608, 4727, 9454, 18908, 37816

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75628 and 75632. The biggest common factor number is the GCF number.
So the greatest common factor 75628 and 75632 is 4.

Also check out the Least Common Multiple of 75628 and 75632