What is the Greatest Common Factor of 35714 and 35728?

Greatest common factor (GCF) of 35714 and 35728 is 14.

GCF(35714,35728) = 14

We will now calculate the prime factors of 35714 and 35728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35714 and 35728.

How to find the GCF of 35714 and 35728?

We will first find the prime factorization of 35714 and 35728. After we will calculate the factors of 35714 and 35728 and find the biggest common factor number .

Step-1: Prime Factorization of 35714

Prime factors of 35714 are 2, 7, 2551. Prime factorization of 35714 in exponential form is:

35714 = 2¹ × 7¹ × 2551¹

Step-2: Prime Factorization of 35728

Prime factors of 35728 are 2, 7, 11, 29. Prime factorization of 35728 in exponential form is:

35728 = 2⁴ × 7¹ × 11¹ × 29¹

Step-3: Factors of 35714

List of positive integer factors of 35714 that divides 35714 without a remainder.

1, 2, 7, 14, 2551, 5102, 17857

Step-4: Factors of 35728

List of positive integer factors of 35728 that divides 35714 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 29, 44, 56, 58, 77, 88, 112, 116, 154, 176, 203, 232, 308, 319, 406, 464, 616, 638, 812, 1232, 1276, 1624, 2233, 2552, 3248, 4466, 5104, 8932, 17864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35714 and 35728. The biggest common factor number is the GCF number.
So the greatest common factor 35714 and 35728 is 14.

Also check out the Least Common Multiple of 35714 and 35728