What is the Greatest Common Factor of 33600 and 33614?

Greatest common factor (GCF) of 33600 and 33614 is 14.

GCF(33600,33614) = 14

We will now calculate the prime factors of 33600 and 33614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33600 and 33614.

How to find the GCF of 33600 and 33614?

We will first find the prime factorization of 33600 and 33614. After we will calculate the factors of 33600 and 33614 and find the biggest common factor number .

Step-1: Prime Factorization of 33600

Prime factors of 33600 are 2, 3, 5, 7. Prime factorization of 33600 in exponential form is:

33600 = 2⁶ × 3¹ × 5² × 7¹

Step-2: Prime Factorization of 33614

Prime factors of 33614 are 2, 7. Prime factorization of 33614 in exponential form is:

33614 = 2¹ × 7⁵

Step-3: Factors of 33600

List of positive integer factors of 33600 that divides 33600 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 400, 420, 448, 480, 525, 560, 600, 672, 700, 800, 840, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 2100, 2240, 2400, 2800, 3360, 4200, 4800, 5600, 6720, 8400, 11200, 16800

Step-4: Factors of 33614

List of positive integer factors of 33614 that divides 33600 without a remainder.

1, 2, 7, 14, 49, 98, 343, 686, 2401, 4802, 16807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33600 and 33614. The biggest common factor number is the GCF number.
So the greatest common factor 33600 and 33614 is 14.

Also check out the Least Common Multiple of 33600 and 33614