What is the Greatest Common Factor of 99750 and 99770?

Greatest common factor (GCF) of 99750 and 99770 is 10.

GCF(99750,99770) = 10

We will now calculate the prime factors of 99750 and 99770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 99750 and 99770.

How to find the GCF of 99750 and 99770?

We will first find the prime factorization of 99750 and 99770. After we will calculate the factors of 99750 and 99770 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 99770

Prime factors of 99770 are 2, 5, 11, 907. Prime factorization of 99770 in exponential form is:

99770 = 2¹ × 5¹ × 11¹ × 907¹

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 99770

List of positive integer factors of 99770 that divides 99750 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 907, 1814, 4535, 9070, 9977, 19954, 49885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 99750 and 99770. The biggest common factor number is the GCF number.
So the greatest common factor 99750 and 99770 is 10.

Also check out the Least Common Multiple of 99750 and 99770