What is the Greatest Common Factor of 34752 and 34770?

Greatest common factor (GCF) of 34752 and 34770 is 6.

GCF(34752,34770) = 6

We will now calculate the prime factors of 34752 and 34770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34752 and 34770.

How to find the GCF of 34752 and 34770?

We will first find the prime factorization of 34752 and 34770. After we will calculate the factors of 34752 and 34770 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34770

Prime factors of 34770 are 2, 3, 5, 19, 61. Prime factorization of 34770 in exponential form is:

34770 = 2¹ × 3¹ × 5¹ × 19¹ × 61¹

Step-3: Factors of 34752

List of positive integer factors of 34752 that divides 34752 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

Step-4: Factors of 34770

List of positive integer factors of 34770 that divides 34752 without a remainder.

1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 61, 95, 114, 122, 183, 190, 285, 305, 366, 570, 610, 915, 1159, 1830, 2318, 3477, 5795, 6954, 11590, 17385

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34752 and 34770. The biggest common factor number is the GCF number.
So the greatest common factor 34752 and 34770 is 6.

Also check out the Least Common Multiple of 34752 and 34770