What is the Greatest Common Factor of 65970 and 65985?

Greatest common factor (GCF) of 65970 and 65985 is 15.

GCF(65970,65985) = 15

We will now calculate the prime factors of 65970 and 65985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65970 and 65985.

How to find the GCF of 65970 and 65985?

We will first find the prime factorization of 65970 and 65985. After we will calculate the factors of 65970 and 65985 and find the biggest common factor number .

Step-1: Prime Factorization of 65970

Prime factors of 65970 are 2, 3, 5, 733. Prime factorization of 65970 in exponential form is:

65970 = 2¹ × 3² × 5¹ × 733¹

Step-2: Prime Factorization of 65985

Prime factors of 65985 are 3, 5, 53, 83. Prime factorization of 65985 in exponential form is:

65985 = 3¹ × 5¹ × 53¹ × 83¹

Step-3: Factors of 65970

List of positive integer factors of 65970 that divides 65970 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 733, 1466, 2199, 3665, 4398, 6597, 7330, 10995, 13194, 21990, 32985

Step-4: Factors of 65985

List of positive integer factors of 65985 that divides 65970 without a remainder.

1, 3, 5, 15, 53, 83, 159, 249, 265, 415, 795, 1245, 4399, 13197, 21995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65970 and 65985. The biggest common factor number is the GCF number.
So the greatest common factor 65970 and 65985 is 15.

Also check out the Least Common Multiple of 65970 and 65985