What is the Greatest Common Factor of 99750 and 99760?

Greatest common factor (GCF) of 99750 and 99760 is 10.

GCF(99750,99760) = 10

We will now calculate the prime factors of 99750 and 99760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 99750 and 99760.

How to find the GCF of 99750 and 99760?

We will first find the prime factorization of 99750 and 99760. After we will calculate the factors of 99750 and 99760 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 99760

Prime factors of 99760 are 2, 5, 29, 43. Prime factorization of 99760 in exponential form is:

99760 = 2⁴ × 5¹ × 29¹ × 43¹

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 99760

List of positive integer factors of 99760 that divides 99750 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 29, 40, 43, 58, 80, 86, 116, 145, 172, 215, 232, 290, 344, 430, 464, 580, 688, 860, 1160, 1247, 1720, 2320, 2494, 3440, 4988, 6235, 9976, 12470, 19952, 24940, 49880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 99750 and 99760. The biggest common factor number is the GCF number.
So the greatest common factor 99750 and 99760 is 10.

Also check out the Least Common Multiple of 99750 and 99760