What is the Greatest Common Factor of 39890 and 39900?

Greatest common factor (GCF) of 39890 and 39900 is 10.

GCF(39890,39900) = 10

We will now calculate the prime factors of 39890 and 39900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39890 and 39900.

How to find the GCF of 39890 and 39900?

We will first find the prime factorization of 39890 and 39900. After we will calculate the factors of 39890 and 39900 and find the biggest common factor number .

Step-1: Prime Factorization of 39890

Prime factors of 39890 are 2, 5, 3989. Prime factorization of 39890 in exponential form is:

39890 = 2¹ × 5¹ × 3989¹

Step-2: Prime Factorization of 39900

Prime factors of 39900 are 2, 3, 5, 7, 19. Prime factorization of 39900 in exponential form is:

39900 = 2² × 3¹ × 5² × 7¹ × 19¹

Step-3: Factors of 39890

List of positive integer factors of 39890 that divides 39890 without a remainder.

1, 2, 5, 10, 3989, 7978, 19945

Step-4: Factors of 39900

List of positive integer factors of 39900 that divides 39890 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 25, 28, 30, 35, 38, 42, 50, 57, 60, 70, 75, 76, 84, 95, 100, 105, 114, 133, 140, 150, 175, 190, 210, 228, 266, 285, 300, 350, 380, 399, 420, 475, 525, 532, 570, 665, 700, 798, 950, 1050, 1140, 1330, 1425, 1596, 1900, 1995, 2100, 2660, 2850, 3325, 3990, 5700, 6650, 7980, 9975, 13300, 19950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39890 and 39900. The biggest common factor number is the GCF number.
So the greatest common factor 39890 and 39900 is 10.

Also check out the Least Common Multiple of 39890 and 39900