What is the Greatest Common Factor of 35805 and 35819?

Greatest common factor (GCF) of 35805 and 35819 is 7.

GCF(35805,35819) = 7

We will now calculate the prime factors of 35805 and 35819, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35805 and 35819.

How to find the GCF of 35805 and 35819?

We will first find the prime factorization of 35805 and 35819. After we will calculate the factors of 35805 and 35819 and find the biggest common factor number .

Step-1: Prime Factorization of 35805

Prime factors of 35805 are 3, 5, 7, 11, 31. Prime factorization of 35805 in exponential form is:

35805 = 3¹ × 5¹ × 7¹ × 11¹ × 31¹

Step-2: Prime Factorization of 35819

Prime factors of 35819 are 7, 17, 43. Prime factorization of 35819 in exponential form is:

35819 = 7² × 17¹ × 43¹

Step-3: Factors of 35805

List of positive integer factors of 35805 that divides 35805 without a remainder.

1, 3, 5, 7, 11, 15, 21, 31, 33, 35, 55, 77, 93, 105, 155, 165, 217, 231, 341, 385, 465, 651, 1023, 1085, 1155, 1705, 2387, 3255, 5115, 7161, 11935

Step-4: Factors of 35819

List of positive integer factors of 35819 that divides 35805 without a remainder.

1, 7, 17, 43, 49, 119, 301, 731, 833, 2107, 5117

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35805 and 35819. The biggest common factor number is the GCF number.
So the greatest common factor 35805 and 35819 is 7.

Also check out the Least Common Multiple of 35805 and 35819