What is the Greatest Common Factor of 39954 and 39960?

Greatest common factor (GCF) of 39954 and 39960 is 6.

GCF(39954,39960) = 6

We will now calculate the prime factors of 39954 and 39960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39954 and 39960.

How to find the GCF of 39954 and 39960?

We will first find the prime factorization of 39954 and 39960. After we will calculate the factors of 39954 and 39960 and find the biggest common factor number .

Step-1: Prime Factorization of 39954

Prime factors of 39954 are 2, 3, 6659. Prime factorization of 39954 in exponential form is:

39954 = 2¹ × 3¹ × 6659¹

Step-2: Prime Factorization of 39960

Prime factors of 39960 are 2, 3, 5, 37. Prime factorization of 39960 in exponential form is:

39960 = 2³ × 3³ × 5¹ × 37¹

Step-3: Factors of 39954

List of positive integer factors of 39954 that divides 39954 without a remainder.

1, 2, 3, 6, 6659, 13318, 19977

Step-4: Factors of 39960

List of positive integer factors of 39960 that divides 39954 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 37, 40, 45, 54, 60, 72, 74, 90, 108, 111, 120, 135, 148, 180, 185, 216, 222, 270, 296, 333, 360, 370, 444, 540, 555, 666, 740, 888, 999, 1080, 1110, 1332, 1480, 1665, 1998, 2220, 2664, 3330, 3996, 4440, 4995, 6660, 7992, 9990, 13320, 19980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39954 and 39960. The biggest common factor number is the GCF number.
So the greatest common factor 39954 and 39960 is 6.

Also check out the Least Common Multiple of 39954 and 39960