What is the Greatest Common Factor of 67536 and 67542?

Greatest common factor (GCF) of 67536 and 67542 is 6.

GCF(67536,67542) = 6

We will now calculate the prime factors of 67536 and 67542, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67536 and 67542.

How to find the GCF of 67536 and 67542?

We will first find the prime factorization of 67536 and 67542. After we will calculate the factors of 67536 and 67542 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 67542

Prime factors of 67542 are 2, 3, 11257. Prime factorization of 67542 in exponential form is:

67542 = 2¹ × 3¹ × 11257¹

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 67542

List of positive integer factors of 67542 that divides 67536 without a remainder.

1, 2, 3, 6, 11257, 22514, 33771

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67536 and 67542. The biggest common factor number is the GCF number.
So the greatest common factor 67536 and 67542 is 6.

Also check out the Least Common Multiple of 67536 and 67542