What is the Greatest Common Factor of 75628 and 75635?

Greatest common factor (GCF) of 75628 and 75635 is 7.

GCF(75628,75635) = 7

We will now calculate the prime factors of 75628 and 75635, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75628 and 75635.

How to find the GCF of 75628 and 75635?

We will first find the prime factorization of 75628 and 75635. After we will calculate the factors of 75628 and 75635 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 75635

Prime factors of 75635 are 5, 7, 2161. Prime factorization of 75635 in exponential form is:

75635 = 5¹ × 7¹ × 2161¹

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 75635

List of positive integer factors of 75635 that divides 75628 without a remainder.

1, 5, 7, 35, 2161, 10805, 15127

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75628 and 75635. The biggest common factor number is the GCF number.
So the greatest common factor 75628 and 75635 is 7.

Also check out the Least Common Multiple of 75628 and 75635