What is the Greatest Common Factor of 34740 and 34752?

Greatest common factor (GCF) of 34740 and 34752 is 12.

GCF(34740,34752) = 12

We will now calculate the prime factors of 34740 and 34752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34740 and 34752.

How to find the GCF of 34740 and 34752?

We will first find the prime factorization of 34740 and 34752. After we will calculate the factors of 34740 and 34752 and find the biggest common factor number .

Step-1: Prime Factorization of 34740

Prime factors of 34740 are 2, 3, 5, 193. Prime factorization of 34740 in exponential form is:

34740 = 2² × 3² × 5¹ × 193¹

Step-2: Prime Factorization of 34752

Prime factors of 34752 are 2, 3, 181. Prime factorization of 34752 in exponential form is:

34752 = 2⁶ × 3¹ × 181¹

Step-3: Factors of 34740

List of positive integer factors of 34740 that divides 34740 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 193, 386, 579, 772, 965, 1158, 1737, 1930, 2316, 2895, 3474, 3860, 5790, 6948, 8685, 11580, 17370

Step-4: Factors of 34752

List of positive integer factors of 34752 that divides 34740 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 181, 192, 362, 543, 724, 1086, 1448, 2172, 2896, 4344, 5792, 8688, 11584, 17376

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34740 and 34752. The biggest common factor number is the GCF number.
So the greatest common factor 34740 and 34752 is 12.

Also check out the Least Common Multiple of 34740 and 34752