What is the Greatest Common Factor of 34500 and 34512?

Greatest common factor (GCF) of 34500 and 34512 is 12.

GCF(34500,34512) = 12

We will now calculate the prime factors of 34500 and 34512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34500 and 34512.

How to find the GCF of 34500 and 34512?

We will first find the prime factorization of 34500 and 34512. After we will calculate the factors of 34500 and 34512 and find the biggest common factor number .

Step-1: Prime Factorization of 34500

Prime factors of 34500 are 2, 3, 5, 23. Prime factorization of 34500 in exponential form is:

34500 = 2² × 3¹ × 5³ × 23¹

Step-2: Prime Factorization of 34512

Prime factors of 34512 are 2, 3, 719. Prime factorization of 34512 in exponential form is:

34512 = 2⁴ × 3¹ × 719¹

Step-3: Factors of 34500

List of positive integer factors of 34500 that divides 34500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 25, 30, 46, 50, 60, 69, 75, 92, 100, 115, 125, 138, 150, 230, 250, 276, 300, 345, 375, 460, 500, 575, 690, 750, 1150, 1380, 1500, 1725, 2300, 2875, 3450, 5750, 6900, 8625, 11500, 17250

Step-4: Factors of 34512

List of positive integer factors of 34512 that divides 34500 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 719, 1438, 2157, 2876, 4314, 5752, 8628, 11504, 17256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34500 and 34512. The biggest common factor number is the GCF number.
So the greatest common factor 34500 and 34512 is 12.

Also check out the Least Common Multiple of 34500 and 34512