What is the Greatest Common Factor of 29680 and 29696?

Greatest common factor (GCF) of 29680 and 29696 is 16.

GCF(29680,29696) = 16

We will now calculate the prime factors of 29680 and 29696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29680 and 29696.

How to find the GCF of 29680 and 29696?

We will first find the prime factorization of 29680 and 29696. After we will calculate the factors of 29680 and 29696 and find the biggest common factor number .

Step-1: Prime Factorization of 29680

Prime factors of 29680 are 2, 5, 7, 53. Prime factorization of 29680 in exponential form is:

29680 = 2⁴ × 5¹ × 7¹ × 53¹

Step-2: Prime Factorization of 29696

Prime factors of 29696 are 2, 29. Prime factorization of 29696 in exponential form is:

29696 = 2¹⁰ × 29¹

Step-3: Factors of 29680

List of positive integer factors of 29680 that divides 29680 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 53, 56, 70, 80, 106, 112, 140, 212, 265, 280, 371, 424, 530, 560, 742, 848, 1060, 1484, 1855, 2120, 2968, 3710, 4240, 5936, 7420, 14840

Step-4: Factors of 29696

List of positive integer factors of 29696 that divides 29680 without a remainder.

1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 256, 464, 512, 928, 1024, 1856, 3712, 7424, 14848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29680 and 29696. The biggest common factor number is the GCF number.
So the greatest common factor 29680 and 29696 is 16.

Also check out the Least Common Multiple of 29680 and 29696