What is the Greatest Common Factor of 65925 and 65940?

Greatest common factor (GCF) of 65925 and 65940 is 15.

GCF(65925,65940) = 15

We will now calculate the prime factors of 65925 and 65940, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65925 and 65940.

How to find the GCF of 65925 and 65940?

We will first find the prime factorization of 65925 and 65940. After we will calculate the factors of 65925 and 65940 and find the biggest common factor number .

Step-1: Prime Factorization of 65925

Prime factors of 65925 are 3, 5, 293. Prime factorization of 65925 in exponential form is:

65925 = 3² × 5² × 293¹

Step-2: Prime Factorization of 65940

Prime factors of 65940 are 2, 3, 5, 7, 157. Prime factorization of 65940 in exponential form is:

65940 = 2² × 3¹ × 5¹ × 7¹ × 157¹

Step-3: Factors of 65925

List of positive integer factors of 65925 that divides 65925 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 225, 293, 879, 1465, 2637, 4395, 7325, 13185, 21975

Step-4: Factors of 65940

List of positive integer factors of 65940 that divides 65925 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 157, 210, 314, 420, 471, 628, 785, 942, 1099, 1570, 1884, 2198, 2355, 3140, 3297, 4396, 4710, 5495, 6594, 9420, 10990, 13188, 16485, 21980, 32970

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65925 and 65940. The biggest common factor number is the GCF number.
So the greatest common factor 65925 and 65940 is 15.

Also check out the Least Common Multiple of 65925 and 65940