What is the Greatest Common Factor of 35296 and 35310?

Greatest common factor (GCF) of 35296 and 35310 is 2.

GCF(35296,35310) = 2

We will now calculate the prime factors of 35296 and 35310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35296 and 35310.

How to find the GCF of 35296 and 35310?

We will first find the prime factorization of 35296 and 35310. After we will calculate the factors of 35296 and 35310 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 35310

Prime factors of 35310 are 2, 3, 5, 11, 107. Prime factorization of 35310 in exponential form is:

35310 = 2¹ × 3¹ × 5¹ × 11¹ × 107¹

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 35310

List of positive integer factors of 35310 that divides 35296 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 107, 110, 165, 214, 321, 330, 535, 642, 1070, 1177, 1605, 2354, 3210, 3531, 5885, 7062, 11770, 17655

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35296 and 35310. The biggest common factor number is the GCF number.
So the greatest common factor 35296 and 35310 is 2.

Also check out the Least Common Multiple of 35296 and 35310