What is the Greatest Common Factor of 9750 and 9760?

Greatest common factor (GCF) of 9750 and 9760 is 10.

GCF(9750,9760) = 10

We will now calculate the prime factors of 9750 and 9760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9750 and 9760.

How to find the GCF of 9750 and 9760?

We will first find the prime factorization of 9750 and 9760. After we will calculate the factors of 9750 and 9760 and find the biggest common factor number .

Step-1: Prime Factorization of 9750

Prime factors of 9750 are 2, 3, 5, 13. Prime factorization of 9750 in exponential form is:

9750 = 2¹ × 3¹ × 5³ × 13¹

Step-2: Prime Factorization of 9760

Prime factors of 9760 are 2, 5, 61. Prime factorization of 9760 in exponential form is:

9760 = 2⁵ × 5¹ × 61¹

Step-3: Factors of 9750

List of positive integer factors of 9750 that divides 9750 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875

Step-4: Factors of 9760

List of positive integer factors of 9760 that divides 9750 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 61, 80, 122, 160, 244, 305, 488, 610, 976, 1220, 1952, 2440, 4880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9750 and 9760. The biggest common factor number is the GCF number.
So the greatest common factor 9750 and 9760 is 10.

Also check out the Least Common Multiple of 9750 and 9760