What is the Greatest Common Factor of 35854 and 35872?

Greatest common factor (GCF) of 35854 and 35872 is 2.

GCF(35854,35872) = 2

We will now calculate the prime factors of 35854 and 35872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35854 and 35872.

How to find the GCF of 35854 and 35872?

We will first find the prime factorization of 35854 and 35872. After we will calculate the factors of 35854 and 35872 and find the biggest common factor number .

Step-1: Prime Factorization of 35854

Prime factors of 35854 are 2, 7, 13, 197. Prime factorization of 35854 in exponential form is:

35854 = 2¹ × 7¹ × 13¹ × 197¹

Step-2: Prime Factorization of 35872

Prime factors of 35872 are 2, 19, 59. Prime factorization of 35872 in exponential form is:

35872 = 2⁵ × 19¹ × 59¹

Step-3: Factors of 35854

List of positive integer factors of 35854 that divides 35854 without a remainder.

1, 2, 7, 13, 14, 26, 91, 182, 197, 394, 1379, 2561, 2758, 5122, 17927

Step-4: Factors of 35872

List of positive integer factors of 35872 that divides 35854 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 59, 76, 118, 152, 236, 304, 472, 608, 944, 1121, 1888, 2242, 4484, 8968, 17936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35854 and 35872. The biggest common factor number is the GCF number.
So the greatest common factor 35854 and 35872 is 2.

Also check out the Least Common Multiple of 35854 and 35872