What is the Greatest Common Factor of 67552 and 67564?

Greatest common factor (GCF) of 67552 and 67564 is 4.

GCF(67552,67564) = 4

We will now calculate the prime factors of 67552 and 67564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67552 and 67564.

How to find the GCF of 67552 and 67564?

We will first find the prime factorization of 67552 and 67564. After we will calculate the factors of 67552 and 67564 and find the biggest common factor number .

Step-1: Prime Factorization of 67552

Prime factors of 67552 are 2, 2111. Prime factorization of 67552 in exponential form is:

67552 = 2⁵ × 2111¹

Step-2: Prime Factorization of 67564

Prime factors of 67564 are 2, 7, 19, 127. Prime factorization of 67564 in exponential form is:

67564 = 2² × 7¹ × 19¹ × 127¹

Step-3: Factors of 67552

List of positive integer factors of 67552 that divides 67552 without a remainder.

1, 2, 4, 8, 16, 32, 2111, 4222, 8444, 16888, 33776

Step-4: Factors of 67564

List of positive integer factors of 67564 that divides 67552 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 76, 127, 133, 254, 266, 508, 532, 889, 1778, 2413, 3556, 4826, 9652, 16891, 33782

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67552 and 67564. The biggest common factor number is the GCF number.
So the greatest common factor 67552 and 67564 is 4.

Also check out the Least Common Multiple of 67552 and 67564