What is the Greatest Common Factor of 67560 and 67575?

Greatest common factor (GCF) of 67560 and 67575 is 15.

GCF(67560,67575) = 15

We will now calculate the prime factors of 67560 and 67575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67560 and 67575.

How to find the GCF of 67560 and 67575?

We will first find the prime factorization of 67560 and 67575. After we will calculate the factors of 67560 and 67575 and find the biggest common factor number .

Step-1: Prime Factorization of 67560

Prime factors of 67560 are 2, 3, 5, 563. Prime factorization of 67560 in exponential form is:

67560 = 2³ × 3¹ × 5¹ × 563¹

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 67560

List of positive integer factors of 67560 that divides 67560 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 563, 1126, 1689, 2252, 2815, 3378, 4504, 5630, 6756, 8445, 11260, 13512, 16890, 22520, 33780

Step-4: Factors of 67575

List of positive integer factors of 67575 that divides 67560 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 67560 and 67575. The biggest common factor number is the GCF number.
So the greatest common factor 67560 and 67575 is 15.

Also check out the Least Common Multiple of 67560 and 67575