What is the Greatest Common Factor of 39764 and 39780?

Greatest common factor (GCF) of 39764 and 39780 is 4.

GCF(39764,39780) = 4

We will now calculate the prime factors of 39764 and 39780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39764 and 39780.

How to find the GCF of 39764 and 39780?

We will first find the prime factorization of 39764 and 39780. After we will calculate the factors of 39764 and 39780 and find the biggest common factor number .

Step-1: Prime Factorization of 39764

Prime factors of 39764 are 2, 9941. Prime factorization of 39764 in exponential form is:

39764 = 2² × 9941¹

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 39764

List of positive integer factors of 39764 that divides 39764 without a remainder.

1, 2, 4, 9941, 19882

Step-4: Factors of 39780

List of positive integer factors of 39780 that divides 39764 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 39764 and 39780. The biggest common factor number is the GCF number.
So the greatest common factor 39764 and 39780 is 4.

Also check out the Least Common Multiple of 39764 and 39780