What is the Greatest Common Factor of 29600 and 29614?

Greatest common factor (GCF) of 29600 and 29614 is 2.

GCF(29600,29614) = 2

We will now calculate the prime factors of 29600 and 29614, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29600 and 29614.

How to find the GCF of 29600 and 29614?

We will first find the prime factorization of 29600 and 29614. After we will calculate the factors of 29600 and 29614 and find the biggest common factor number .

Step-1: Prime Factorization of 29600

Prime factors of 29600 are 2, 5, 37. Prime factorization of 29600 in exponential form is:

29600 = 2⁵ × 5² × 37¹

Step-2: Prime Factorization of 29614

Prime factors of 29614 are 2, 13, 17, 67. Prime factorization of 29614 in exponential form is:

29614 = 2¹ × 13¹ × 17¹ × 67¹

Step-3: Factors of 29600

List of positive integer factors of 29600 that divides 29600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 37, 40, 50, 74, 80, 100, 148, 160, 185, 200, 296, 370, 400, 592, 740, 800, 925, 1184, 1480, 1850, 2960, 3700, 5920, 7400, 14800

Step-4: Factors of 29614

List of positive integer factors of 29614 that divides 29600 without a remainder.

1, 2, 13, 17, 26, 34, 67, 134, 221, 442, 871, 1139, 1742, 2278, 14807

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29600 and 29614. The biggest common factor number is the GCF number.
So the greatest common factor 29600 and 29614 is 2.

Also check out the Least Common Multiple of 29600 and 29614