What is the Greatest Common Factor of 35314 and 35328?

Greatest common factor (GCF) of 35314 and 35328 is 2.

GCF(35314,35328) = 2

We will now calculate the prime factors of 35314 and 35328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35314 and 35328.

How to find the GCF of 35314 and 35328?

We will first find the prime factorization of 35314 and 35328. After we will calculate the factors of 35314 and 35328 and find the biggest common factor number .

Step-1: Prime Factorization of 35314

Prime factors of 35314 are 2, 17657. Prime factorization of 35314 in exponential form is:

35314 = 2¹ × 17657¹

Step-2: Prime Factorization of 35328

Prime factors of 35328 are 2, 3, 23. Prime factorization of 35328 in exponential form is:

35328 = 2⁹ × 3¹ × 23¹

Step-3: Factors of 35314

List of positive integer factors of 35314 that divides 35314 without a remainder.

1, 2, 17657

Step-4: Factors of 35328

List of positive integer factors of 35328 that divides 35314 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 64, 69, 92, 96, 128, 138, 184, 192, 256, 276, 368, 384, 512, 552, 736, 768, 1104, 1472, 1536, 2208, 2944, 4416, 5888, 8832, 11776, 17664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35314 and 35328. The biggest common factor number is the GCF number.
So the greatest common factor 35314 and 35328 is 2.

Also check out the Least Common Multiple of 35314 and 35328