What is the Greatest Common Factor of 69966 and 69975?

Greatest common factor (GCF) of 69966 and 69975 is 9.

GCF(69966,69975) = 9

We will now calculate the prime factors of 69966 and 69975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69966 and 69975.

How to find the GCF of 69966 and 69975?

We will first find the prime factorization of 69966 and 69975. After we will calculate the factors of 69966 and 69975 and find the biggest common factor number .

Step-1: Prime Factorization of 69966

Prime factors of 69966 are 2, 3, 13, 23. Prime factorization of 69966 in exponential form is:

69966 = 2¹ × 3² × 13² × 23¹

Step-2: Prime Factorization of 69975

Prime factors of 69975 are 3, 5, 311. Prime factorization of 69975 in exponential form is:

69975 = 3² × 5² × 311¹

Step-3: Factors of 69966

List of positive integer factors of 69966 that divides 69966 without a remainder.

1, 2, 3, 6, 9, 13, 18, 23, 26, 39, 46, 69, 78, 117, 138, 169, 207, 234, 299, 338, 414, 507, 598, 897, 1014, 1521, 1794, 2691, 3042, 3887, 5382, 7774, 11661, 23322, 34983

Step-4: Factors of 69975

List of positive integer factors of 69975 that divides 69966 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 311, 933, 1555, 2799, 4665, 7775, 13995, 23325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69966 and 69975. The biggest common factor number is the GCF number.
So the greatest common factor 69966 and 69975 is 9.

Also check out the Least Common Multiple of 69966 and 69975