What is the Greatest Common Factor of 75628 and 75648?

Greatest common factor (GCF) of 75628 and 75648 is 4.

GCF(75628,75648) = 4

We will now calculate the prime factors of 75628 and 75648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75628 and 75648.

How to find the GCF of 75628 and 75648?

We will first find the prime factorization of 75628 and 75648. After we will calculate the factors of 75628 and 75648 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 75648

Prime factors of 75648 are 2, 3, 197. Prime factorization of 75648 in exponential form is:

75648 = 2⁷ × 3¹ × 197¹

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 75648

List of positive integer factors of 75648 that divides 75628 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 197, 384, 394, 591, 788, 1182, 1576, 2364, 3152, 4728, 6304, 9456, 12608, 18912, 25216, 37824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75628 and 75648. The biggest common factor number is the GCF number.
So the greatest common factor 75628 and 75648 is 4.

Also check out the Least Common Multiple of 75628 and 75648