What is the Greatest Common Factor of 39900 and 39917?

Greatest common factor (GCF) of 39900 and 39917 is 1.

GCF(39900,39917) = 1

We will now calculate the prime factors of 39900 and 39917, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39900 and 39917.

How to find the GCF of 39900 and 39917?

We will first find the prime factorization of 39900 and 39917. After we will calculate the factors of 39900 and 39917 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39917

Prime factors of 39917 are 179, 223. Prime factorization of 39917 in exponential form is:

39917 = 179¹ × 223¹

Step-3: Factors of 39900

List of positive integer factors of 39900 that divides 39900 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

Step-4: Factors of 39917

List of positive integer factors of 39917 that divides 39900 without a remainder.

1, 179, 223

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39900 and 39917. The biggest common factor number is the GCF number.
So the greatest common factor 39900 and 39917 is 1.

Also check out the Least Common Multiple of 39900 and 39917