What is the Greatest Common Factor of 35105 and 35122?

Greatest common factor (GCF) of 35105 and 35122 is 17.

GCF(35105,35122) = 17

We will now calculate the prime factors of 35105 and 35122, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35105 and 35122.

How to find the GCF of 35105 and 35122?

We will first find the prime factorization of 35105 and 35122. After we will calculate the factors of 35105 and 35122 and find the biggest common factor number .

Step-1: Prime Factorization of 35105

Prime factors of 35105 are 5, 7, 17, 59. Prime factorization of 35105 in exponential form is:

35105 = 5¹ × 7¹ × 17¹ × 59¹

Step-2: Prime Factorization of 35122

Prime factors of 35122 are 2, 17, 1033. Prime factorization of 35122 in exponential form is:

35122 = 2¹ × 17¹ × 1033¹

Step-3: Factors of 35105

List of positive integer factors of 35105 that divides 35105 without a remainder.

1, 5, 7, 17, 35, 59, 85, 119, 295, 413, 595, 1003, 2065, 5015, 7021

Step-4: Factors of 35122

List of positive integer factors of 35122 that divides 35105 without a remainder.

1, 2, 17, 34, 1033, 2066, 17561

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35105 and 35122. The biggest common factor number is the GCF number.
So the greatest common factor 35105 and 35122 is 17.

Also check out the Least Common Multiple of 35105 and 35122