What is the Greatest Common Factor of 38752 and 38766?

Greatest common factor (GCF) of 38752 and 38766 is 14.

GCF(38752,38766) = 14

We will now calculate the prime factors of 38752 and 38766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38752 and 38766.

How to find the GCF of 38752 and 38766?

We will first find the prime factorization of 38752 and 38766. After we will calculate the factors of 38752 and 38766 and find the biggest common factor number .

Step-1: Prime Factorization of 38752

Prime factors of 38752 are 2, 7, 173. Prime factorization of 38752 in exponential form is:

38752 = 2⁵ × 7¹ × 173¹

Step-2: Prime Factorization of 38766

Prime factors of 38766 are 2, 3, 7, 13, 71. Prime factorization of 38766 in exponential form is:

38766 = 2¹ × 3¹ × 7¹ × 13¹ × 71¹

Step-3: Factors of 38752

List of positive integer factors of 38752 that divides 38752 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 173, 224, 346, 692, 1211, 1384, 2422, 2768, 4844, 5536, 9688, 19376

Step-4: Factors of 38766

List of positive integer factors of 38766 that divides 38752 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 71, 78, 91, 142, 182, 213, 273, 426, 497, 546, 923, 994, 1491, 1846, 2769, 2982, 5538, 6461, 12922, 19383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38752 and 38766. The biggest common factor number is the GCF number.
So the greatest common factor 38752 and 38766 is 14.

Also check out the Least Common Multiple of 38752 and 38766