What is the Greatest Common Factor of 67725 and 67740?

Greatest common factor (GCF) of 67725 and 67740 is 15.

GCF(67725,67740) = 15

We will now calculate the prime factors of 67725 and 67740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67725 and 67740.

How to find the GCF of 67725 and 67740?

We will first find the prime factorization of 67725 and 67740. After we will calculate the factors of 67725 and 67740 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 67740

Prime factors of 67740 are 2, 3, 5, 1129. Prime factorization of 67740 in exponential form is:

67740 = 2² × 3¹ × 5¹ × 1129¹

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 67740

List of positive integer factors of 67740 that divides 67725 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1129, 2258, 3387, 4516, 5645, 6774, 11290, 13548, 16935, 22580, 33870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67725 and 67740. The biggest common factor number is the GCF number.
So the greatest common factor 67725 and 67740 is 15.

Also check out the Least Common Multiple of 67725 and 67740