What is the Greatest Common Factor of 29600 and 29616?

Greatest common factor (GCF) of 29600 and 29616 is 16.

GCF(29600,29616) = 16

We will now calculate the prime factors of 29600 and 29616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29600 and 29616.

How to find the GCF of 29600 and 29616?

We will first find the prime factorization of 29600 and 29616. After we will calculate the factors of 29600 and 29616 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 29616

Prime factors of 29616 are 2, 3, 617. Prime factorization of 29616 in exponential form is:

29616 = 2⁴ × 3¹ × 617¹

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 29616

List of positive integer factors of 29616 that divides 29600 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 617, 1234, 1851, 2468, 3702, 4936, 7404, 9872, 14808

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29600 and 29616. The biggest common factor number is the GCF number.
So the greatest common factor 29600 and 29616 is 16.

Also check out the Least Common Multiple of 29600 and 29616