What is the Greatest Common Factor of 39732 and 39746?

Greatest common factor (GCF) of 39732 and 39746 is 14.

GCF(39732,39746) = 14

We will now calculate the prime factors of 39732 and 39746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39732 and 39746.

How to find the GCF of 39732 and 39746?

We will first find the prime factorization of 39732 and 39746. After we will calculate the factors of 39732 and 39746 and find the biggest common factor number .

Step-1: Prime Factorization of 39732

Prime factors of 39732 are 2, 3, 7, 11, 43. Prime factorization of 39732 in exponential form is:

39732 = 2² × 3¹ × 7¹ × 11¹ × 43¹

Step-2: Prime Factorization of 39746

Prime factors of 39746 are 2, 7, 17, 167. Prime factorization of 39746 in exponential form is:

39746 = 2¹ × 7¹ × 17¹ × 167¹

Step-3: Factors of 39732

List of positive integer factors of 39732 that divides 39732 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 43, 44, 66, 77, 84, 86, 129, 132, 154, 172, 231, 258, 301, 308, 462, 473, 516, 602, 903, 924, 946, 1204, 1419, 1806, 1892, 2838, 3311, 3612, 5676, 6622, 9933, 13244, 19866

Step-4: Factors of 39746

List of positive integer factors of 39746 that divides 39732 without a remainder.

1, 2, 7, 14, 17, 34, 119, 167, 238, 334, 1169, 2338, 2839, 5678, 19873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39732 and 39746. The biggest common factor number is the GCF number.
So the greatest common factor 39732 and 39746 is 14.

Also check out the Least Common Multiple of 39732 and 39746