What is the Greatest Common Factor of 67569 and 67575?

Greatest common factor (GCF) of 67569 and 67575 is 3.

GCF(67569,67575) = 3

We will now calculate the prime factors of 67569 and 67575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67569 and 67575.

How to find the GCF of 67569 and 67575?

We will first find the prime factorization of 67569 and 67575. After we will calculate the factors of 67569 and 67575 and find the biggest common factor number .

Step-1: Prime Factorization of 67569

Prime factors of 67569 are 3, 101, 223. Prime factorization of 67569 in exponential form is:

67569 = 3¹ × 101¹ × 223¹

Step-2: Prime Factorization of 67575

Prime factors of 67575 are 3, 5, 17, 53. Prime factorization of 67575 in exponential form is:

67575 = 3¹ × 5² × 17¹ × 53¹

Step-3: Factors of 67569

List of positive integer factors of 67569 that divides 67569 without a remainder.

1, 3, 101, 223, 303, 669, 22523

Step-4: Factors of 67575

List of positive integer factors of 67575 that divides 67569 without a remainder.

1, 3, 5, 15, 17, 25, 51, 53, 75, 85, 159, 255, 265, 425, 795, 901, 1275, 1325, 2703, 3975, 4505, 13515, 22525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67569 and 67575. The biggest common factor number is the GCF number.
So the greatest common factor 67569 and 67575 is 3.

Also check out the Least Common Multiple of 67569 and 67575