What is the Greatest Common Factor of 39768 and 39780?

Greatest common factor (GCF) of 39768 and 39780 is 12.

GCF(39768,39780) = 12

We will now calculate the prime factors of 39768 and 39780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39768 and 39780.

How to find the GCF of 39768 and 39780?

We will first find the prime factorization of 39768 and 39780. After we will calculate the factors of 39768 and 39780 and find the biggest common factor number .

Step-1: Prime Factorization of 39768

Prime factors of 39768 are 2, 3, 1657. Prime factorization of 39768 in exponential form is:

39768 = 2³ × 3¹ × 1657¹

Step-2: Prime Factorization of 39780

Prime factors of 39780 are 2, 3, 5, 13, 17. Prime factorization of 39780 in exponential form is:

39780 = 2² × 3² × 5¹ × 13¹ × 17¹

Step-3: Factors of 39768

List of positive integer factors of 39768 that divides 39768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1657, 3314, 4971, 6628, 9942, 13256, 19884

Step-4: Factors of 39780

List of positive integer factors of 39780 that divides 39768 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 17, 18, 20, 26, 30, 34, 36, 39, 45, 51, 52, 60, 65, 68, 78, 85, 90, 102, 117, 130, 153, 156, 170, 180, 195, 204, 221, 234, 255, 260, 306, 340, 390, 442, 468, 510, 585, 612, 663, 765, 780, 884, 1020, 1105, 1170, 1326, 1530, 1989, 2210, 2340, 2652, 3060, 3315, 3978, 4420, 6630, 7956, 9945, 13260, 19890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39768 and 39780. The biggest common factor number is the GCF number.
So the greatest common factor 39768 and 39780 is 12.

Also check out the Least Common Multiple of 39768 and 39780