What is the Greatest Common Factor of 67725 and 67730?

Greatest common factor (GCF) of 67725 and 67730 is 5.

GCF(67725,67730) = 5

We will now calculate the prime factors of 67725 and 67730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67725 and 67730.

How to find the GCF of 67725 and 67730?

We will first find the prime factorization of 67725 and 67730. After we will calculate the factors of 67725 and 67730 and find the biggest common factor number .

Step-1: Prime Factorization of 67725

Prime factors of 67725 are 3, 5, 7, 43. Prime factorization of 67725 in exponential form is:

67725 = 3² × 5² × 7¹ × 43¹

Step-2: Prime Factorization of 67730

Prime factors of 67730 are 2, 5, 13, 521. Prime factorization of 67730 in exponential form is:

67730 = 2¹ × 5¹ × 13¹ × 521¹

Step-3: Factors of 67725

List of positive integer factors of 67725 that divides 67725 without a remainder.

1, 3, 5, 7, 9, 15, 21, 25, 35, 43, 45, 63, 75, 105, 129, 175, 215, 225, 301, 315, 387, 525, 645, 903, 1075, 1505, 1575, 1935, 2709, 3225, 4515, 7525, 9675, 13545, 22575

Step-4: Factors of 67730

List of positive integer factors of 67730 that divides 67725 without a remainder.

1, 2, 5, 10, 13, 26, 65, 130, 521, 1042, 2605, 5210, 6773, 13546, 33865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67725 and 67730. The biggest common factor number is the GCF number.
So the greatest common factor 67725 and 67730 is 5.

Also check out the Least Common Multiple of 67725 and 67730