What is the Greatest Common Factor of 69105 and 69114?

Greatest common factor (GCF) of 69105 and 69114 is 3.

GCF(69105,69114) = 3

We will now calculate the prime factors of 69105 and 69114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69105 and 69114.

How to find the GCF of 69105 and 69114?

We will first find the prime factorization of 69105 and 69114. After we will calculate the factors of 69105 and 69114 and find the biggest common factor number .

Step-1: Prime Factorization of 69105

Prime factors of 69105 are 3, 5, 17, 271. Prime factorization of 69105 in exponential form is:

69105 = 3¹ × 5¹ × 17¹ × 271¹

Step-2: Prime Factorization of 69114

Prime factors of 69114 are 2, 3, 11519. Prime factorization of 69114 in exponential form is:

69114 = 2¹ × 3¹ × 11519¹

Step-3: Factors of 69105

List of positive integer factors of 69105 that divides 69105 without a remainder.

1, 3, 5, 15, 17, 51, 85, 255, 271, 813, 1355, 4065, 4607, 13821, 23035

Step-4: Factors of 69114

List of positive integer factors of 69114 that divides 69105 without a remainder.

1, 2, 3, 6, 11519, 23038, 34557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69105 and 69114. The biggest common factor number is the GCF number.
So the greatest common factor 69105 and 69114 is 3.

Also check out the Least Common Multiple of 69105 and 69114