What is the Greatest Common Factor of 67536 and 67540?

Greatest common factor (GCF) of 67536 and 67540 is 4.

GCF(67536,67540) = 4

We will now calculate the prime factors of 67536 and 67540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67536 and 67540.

How to find the GCF of 67536 and 67540?

We will first find the prime factorization of 67536 and 67540. After we will calculate the factors of 67536 and 67540 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 67540

Prime factors of 67540 are 2, 5, 11, 307. Prime factorization of 67540 in exponential form is:

67540 = 2² × 5¹ × 11¹ × 307¹

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 67540

List of positive integer factors of 67540 that divides 67536 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220, 307, 614, 1228, 1535, 3070, 3377, 6140, 6754, 13508, 16885, 33770

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67536 and 67540. The biggest common factor number is the GCF number.
So the greatest common factor 67536 and 67540 is 4.

Also check out the Least Common Multiple of 67536 and 67540