What is the Greatest Common Factor of 35584 and 35600?

Greatest common factor (GCF) of 35584 and 35600 is 16.

GCF(35584,35600) = 16

We will now calculate the prime factors of 35584 and 35600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35584 and 35600.

How to find the GCF of 35584 and 35600?

We will first find the prime factorization of 35584 and 35600. After we will calculate the factors of 35584 and 35600 and find the biggest common factor number .

Step-1: Prime Factorization of 35584

Prime factors of 35584 are 2, 139. Prime factorization of 35584 in exponential form is:

35584 = 2⁸ × 139¹

Step-2: Prime Factorization of 35600

Prime factors of 35600 are 2, 5, 89. Prime factorization of 35600 in exponential form is:

35600 = 2⁴ × 5² × 89¹

Step-3: Factors of 35584

List of positive integer factors of 35584 that divides 35584 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 139, 256, 278, 556, 1112, 2224, 4448, 8896, 17792

Step-4: Factors of 35600

List of positive integer factors of 35600 that divides 35584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 89, 100, 178, 200, 356, 400, 445, 712, 890, 1424, 1780, 2225, 3560, 4450, 7120, 8900, 17800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35584 and 35600. The biggest common factor number is the GCF number.
So the greatest common factor 35584 and 35600 is 16.

Also check out the Least Common Multiple of 35584 and 35600