What is the Greatest Common Factor of 39960 and 39970?

Greatest common factor (GCF) of 39960 and 39970 is 10.

GCF(39960,39970) = 10

We will now calculate the prime factors of 39960 and 39970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39960 and 39970.

How to find the GCF of 39960 and 39970?

We will first find the prime factorization of 39960 and 39970. After we will calculate the factors of 39960 and 39970 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39970

Prime factors of 39970 are 2, 5, 7, 571. Prime factorization of 39970 in exponential form is:

39970 = 2¹ × 5¹ × 7¹ × 571¹

Step-3: Factors of 39960

List of positive integer factors of 39960 that divides 39960 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

Step-4: Factors of 39970

List of positive integer factors of 39970 that divides 39960 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 571, 1142, 2855, 3997, 5710, 7994, 19985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39960 and 39970. The biggest common factor number is the GCF number.
So the greatest common factor 39960 and 39970 is 10.

Also check out the Least Common Multiple of 39960 and 39970