What is the Greatest Common Factor of 67509 and 67524?

Greatest common factor (GCF) of 67509 and 67524 is 3.

GCF(67509,67524) = 3

We will now calculate the prime factors of 67509 and 67524, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67509 and 67524.

How to find the GCF of 67509 and 67524?

We will first find the prime factorization of 67509 and 67524. After we will calculate the factors of 67509 and 67524 and find the biggest common factor number .

Step-1: Prime Factorization of 67509

Prime factors of 67509 are 3, 13, 577. Prime factorization of 67509 in exponential form is:

67509 = 3² × 13¹ × 577¹

Step-2: Prime Factorization of 67524

Prime factors of 67524 are 2, 3, 17, 331. Prime factorization of 67524 in exponential form is:

67524 = 2² × 3¹ × 17¹ × 331¹

Step-3: Factors of 67509

List of positive integer factors of 67509 that divides 67509 without a remainder.

1, 3, 9, 13, 39, 117, 577, 1731, 5193, 7501, 22503

Step-4: Factors of 67524

List of positive integer factors of 67524 that divides 67509 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204, 331, 662, 993, 1324, 1986, 3972, 5627, 11254, 16881, 22508, 33762

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67509 and 67524. The biggest common factor number is the GCF number.
So the greatest common factor 67509 and 67524 is 3.

Also check out the Least Common Multiple of 67509 and 67524