What is the Greatest Common Factor of 58734 and 58752?

Greatest common factor (GCF) of 58734 and 58752 is 18.

GCF(58734,58752) = 18

We will now calculate the prime factors of 58734 and 58752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58734 and 58752.

How to find the GCF of 58734 and 58752?

We will first find the prime factorization of 58734 and 58752. After we will calculate the factors of 58734 and 58752 and find the biggest common factor number .

Step-1: Prime Factorization of 58734

Prime factors of 58734 are 2, 3, 13, 251. Prime factorization of 58734 in exponential form is:

58734 = 2¹ × 3² × 13¹ × 251¹

Step-2: Prime Factorization of 58752

Prime factors of 58752 are 2, 3, 17. Prime factorization of 58752 in exponential form is:

58752 = 2⁷ × 3³ × 17¹

Step-3: Factors of 58734

List of positive integer factors of 58734 that divides 58734 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234, 251, 502, 753, 1506, 2259, 3263, 4518, 6526, 9789, 19578, 29367

Step-4: Factors of 58752

List of positive integer factors of 58752 that divides 58734 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36, 48, 51, 54, 64, 68, 72, 96, 102, 108, 128, 136, 144, 153, 192, 204, 216, 272, 288, 306, 384, 408, 432, 459, 544, 576, 612, 816, 864, 918, 1088, 1152, 1224, 1632, 1728, 1836, 2176, 2448, 3264, 3456, 3672, 4896, 6528, 7344, 9792, 14688, 19584, 29376

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58734 and 58752. The biggest common factor number is the GCF number.
So the greatest common factor 58734 and 58752 is 18.

Also check out the Least Common Multiple of 58734 and 58752