What is the Greatest Common Factor of 66738 and 66752?

Greatest common factor (GCF) of 66738 and 66752 is 14.

GCF(66738,66752) = 14

We will now calculate the prime factors of 66738 and 66752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66738 and 66752.

How to find the GCF of 66738 and 66752?

We will first find the prime factorization of 66738 and 66752. After we will calculate the factors of 66738 and 66752 and find the biggest common factor number .

Step-1: Prime Factorization of 66738

Prime factors of 66738 are 2, 3, 7, 227. Prime factorization of 66738 in exponential form is:

66738 = 2¹ × 3¹ × 7² × 227¹

Step-2: Prime Factorization of 66752

Prime factors of 66752 are 2, 7, 149. Prime factorization of 66752 in exponential form is:

66752 = 2⁶ × 7¹ × 149¹

Step-3: Factors of 66738

List of positive integer factors of 66738 that divides 66738 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 227, 294, 454, 681, 1362, 1589, 3178, 4767, 9534, 11123, 22246, 33369

Step-4: Factors of 66752

List of positive integer factors of 66752 that divides 66738 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 149, 224, 298, 448, 596, 1043, 1192, 2086, 2384, 4172, 4768, 8344, 9536, 16688, 33376

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66738 and 66752. The biggest common factor number is the GCF number.
So the greatest common factor 66738 and 66752 is 14.

Also check out the Least Common Multiple of 66738 and 66752