What is the Greatest Common Factor of 26509 and 26523?

Greatest common factor (GCF) of 26509 and 26523 is 7.

GCF(26509,26523) = 7

We will now calculate the prime factors of 26509 and 26523, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26509 and 26523.

How to find the GCF of 26509 and 26523?

We will first find the prime factorization of 26509 and 26523. After we will calculate the factors of 26509 and 26523 and find the biggest common factor number .

Step-1: Prime Factorization of 26509

Prime factors of 26509 are 7, 541. Prime factorization of 26509 in exponential form is:

26509 = 7² × 541¹

Step-2: Prime Factorization of 26523

Prime factors of 26523 are 3, 7, 421. Prime factorization of 26523 in exponential form is:

26523 = 3² × 7¹ × 421¹

Step-3: Factors of 26509

List of positive integer factors of 26509 that divides 26509 without a remainder.

1, 7, 49, 541, 3787

Step-4: Factors of 26523

List of positive integer factors of 26523 that divides 26509 without a remainder.

1, 3, 7, 9, 21, 63, 421, 1263, 2947, 3789, 8841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26509 and 26523. The biggest common factor number is the GCF number.
So the greatest common factor 26509 and 26523 is 7.

Also check out the Least Common Multiple of 26509 and 26523