What is the Greatest Common Factor of 34029 and 34048?

Greatest common factor (GCF) of 34029 and 34048 is 19.

GCF(34029,34048) = 19

We will now calculate the prime factors of 34029 and 34048, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34029 and 34048.

How to find the GCF of 34029 and 34048?

We will first find the prime factorization of 34029 and 34048. After we will calculate the factors of 34029 and 34048 and find the biggest common factor number .

Step-1: Prime Factorization of 34029

Prime factors of 34029 are 3, 19, 199. Prime factorization of 34029 in exponential form is:

34029 = 3² × 19¹ × 199¹

Step-2: Prime Factorization of 34048

Prime factors of 34048 are 2, 7, 19. Prime factorization of 34048 in exponential form is:

34048 = 2⁸ × 7¹ × 19¹

Step-3: Factors of 34029

List of positive integer factors of 34029 that divides 34029 without a remainder.

1, 3, 9, 19, 57, 171, 199, 597, 1791, 3781, 11343

Step-4: Factors of 34048

List of positive integer factors of 34048 that divides 34029 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 32, 38, 56, 64, 76, 112, 128, 133, 152, 224, 256, 266, 304, 448, 532, 608, 896, 1064, 1216, 1792, 2128, 2432, 4256, 4864, 8512, 17024

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34029 and 34048. The biggest common factor number is the GCF number.
So the greatest common factor 34029 and 34048 is 19.

Also check out the Least Common Multiple of 34029 and 34048