What is the Greatest Common Factor of 35296 and 35312?

Greatest common factor (GCF) of 35296 and 35312 is 16.

GCF(35296,35312) = 16

We will now calculate the prime factors of 35296 and 35312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35296 and 35312.

How to find the GCF of 35296 and 35312?

We will first find the prime factorization of 35296 and 35312. After we will calculate the factors of 35296 and 35312 and find the biggest common factor number .

Step-1: Prime Factorization of 35296

Prime factors of 35296 are 2, 1103. Prime factorization of 35296 in exponential form is:

35296 = 2⁵ × 1103¹

Step-2: Prime Factorization of 35312

Prime factors of 35312 are 2, 2207. Prime factorization of 35312 in exponential form is:

35312 = 2⁴ × 2207¹

Step-3: Factors of 35296

List of positive integer factors of 35296 that divides 35296 without a remainder.

1, 2, 4, 8, 16, 32, 1103, 2206, 4412, 8824, 17648

Step-4: Factors of 35312

List of positive integer factors of 35312 that divides 35296 without a remainder.

1, 2, 4, 8, 16, 2207, 4414, 8828, 17656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35296 and 35312. The biggest common factor number is the GCF number.
So the greatest common factor 35296 and 35312 is 16.

Also check out the Least Common Multiple of 35296 and 35312