What is the Greatest Common Factor of 26985 and 26999?

Greatest common factor (GCF) of 26985 and 26999 is 7.

GCF(26985,26999) = 7

We will now calculate the prime factors of 26985 and 26999, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26985 and 26999.

How to find the GCF of 26985 and 26999?

We will first find the prime factorization of 26985 and 26999. After we will calculate the factors of 26985 and 26999 and find the biggest common factor number .

Step-1: Prime Factorization of 26985

Prime factors of 26985 are 3, 5, 7, 257. Prime factorization of 26985 in exponential form is:

26985 = 3¹ × 5¹ × 7¹ × 257¹

Step-2: Prime Factorization of 26999

Prime factors of 26999 are 7, 19, 29. Prime factorization of 26999 in exponential form is:

26999 = 7² × 19¹ × 29¹

Step-3: Factors of 26985

List of positive integer factors of 26985 that divides 26985 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 257, 771, 1285, 1799, 3855, 5397, 8995

Step-4: Factors of 26999

List of positive integer factors of 26999 that divides 26985 without a remainder.

1, 7, 19, 29, 49, 133, 203, 551, 931, 1421, 3857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26985 and 26999. The biggest common factor number is the GCF number.
So the greatest common factor 26985 and 26999 is 7.

Also check out the Least Common Multiple of 26985 and 26999