What is the Greatest Common Factor of 99750 and 99764?

Greatest common factor (GCF) of 99750 and 99764 is 14.

GCF(99750,99764) = 14

We will now calculate the prime factors of 99750 and 99764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 99750 and 99764.

How to find the GCF of 99750 and 99764?

We will first find the prime factorization of 99750 and 99764. After we will calculate the factors of 99750 and 99764 and find the biggest common factor number .

Step-1: Prime Factorization of 99750

Prime factors of 99750 are 2, 3, 5, 7, 19. Prime factorization of 99750 in exponential form is:

99750 = 2¹ × 3¹ × 5³ × 7¹ × 19¹

Step-2: Prime Factorization of 99764

Prime factors of 99764 are 2, 7, 509. Prime factorization of 99764 in exponential form is:

99764 = 2² × 7² × 509¹

Step-3: Factors of 99750

List of positive integer factors of 99750 that divides 99750 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 19, 21, 25, 30, 35, 38, 42, 50, 57, 70, 75, 95, 105, 114, 125, 133, 150, 175, 190, 210, 250, 266, 285, 350, 375, 399, 475, 525, 570, 665, 750, 798, 875, 950, 1050, 1330, 1425, 1750, 1995, 2375, 2625, 2850, 3325, 3990, 4750, 5250, 6650, 7125, 9975, 14250, 16625, 19950, 33250, 49875

Step-4: Factors of 99764

List of positive integer factors of 99764 that divides 99750 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196, 509, 1018, 2036, 3563, 7126, 14252, 24941, 49882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 99750 and 99764. The biggest common factor number is the GCF number.
So the greatest common factor 99750 and 99764 is 14.

Also check out the Least Common Multiple of 99750 and 99764