What is the Greatest Common Factor of 67536 and 67550?

Greatest common factor (GCF) of 67536 and 67550 is 14.

GCF(67536,67550) = 14

We will now calculate the prime factors of 67536 and 67550, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67536 and 67550.

How to find the GCF of 67536 and 67550?

We will first find the prime factorization of 67536 and 67550. After we will calculate the factors of 67536 and 67550 and find the biggest common factor number .

Step-1: Prime Factorization of 67536

Prime factors of 67536 are 2, 3, 7, 67. Prime factorization of 67536 in exponential form is:

67536 = 2⁴ × 3² × 7¹ × 67¹

Step-2: Prime Factorization of 67550

Prime factors of 67550 are 2, 5, 7, 193. Prime factorization of 67550 in exponential form is:

67550 = 2¹ × 5² × 7¹ × 193¹

Step-3: Factors of 67536

List of positive integer factors of 67536 that divides 67536 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 67, 72, 84, 112, 126, 134, 144, 168, 201, 252, 268, 336, 402, 469, 504, 536, 603, 804, 938, 1008, 1072, 1206, 1407, 1608, 1876, 2412, 2814, 3216, 3752, 4221, 4824, 5628, 7504, 8442, 9648, 11256, 16884, 22512, 33768

Step-4: Factors of 67550

List of positive integer factors of 67550 that divides 67536 without a remainder.

1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 193, 350, 386, 965, 1351, 1930, 2702, 4825, 6755, 9650, 13510, 33775

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67536 and 67550. The biggest common factor number is the GCF number.
So the greatest common factor 67536 and 67550 is 14.

Also check out the Least Common Multiple of 67536 and 67550