What is the Greatest Common Factor of 34635 and 34650?

Greatest common factor (GCF) of 34635 and 34650 is 15.

GCF(34635,34650) = 15

We will now calculate the prime factors of 34635 and 34650, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34635 and 34650.

How to find the GCF of 34635 and 34650?

We will first find the prime factorization of 34635 and 34650. After we will calculate the factors of 34635 and 34650 and find the biggest common factor number .

Step-1: Prime Factorization of 34635

Prime factors of 34635 are 3, 5, 2309. Prime factorization of 34635 in exponential form is:

34635 = 3¹ × 5¹ × 2309¹

Step-2: Prime Factorization of 34650

Prime factors of 34650 are 2, 3, 5, 7, 11. Prime factorization of 34650 in exponential form is:

34650 = 2¹ × 3² × 5² × 7¹ × 11¹

Step-3: Factors of 34635

List of positive integer factors of 34635 that divides 34635 without a remainder.

1, 3, 5, 15, 2309, 6927, 11545

Step-4: Factors of 34650

List of positive integer factors of 34650 that divides 34635 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 11, 14, 15, 18, 21, 22, 25, 30, 33, 35, 42, 45, 50, 55, 63, 66, 70, 75, 77, 90, 99, 105, 110, 126, 150, 154, 165, 175, 198, 210, 225, 231, 275, 315, 330, 350, 385, 450, 462, 495, 525, 550, 630, 693, 770, 825, 990, 1050, 1155, 1386, 1575, 1650, 1925, 2310, 2475, 3150, 3465, 3850, 4950, 5775, 6930, 11550, 17325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34635 and 34650. The biggest common factor number is the GCF number.
So the greatest common factor 34635 and 34650 is 15.

Also check out the Least Common Multiple of 34635 and 34650