What is the Greatest Common Factor of 21750 and 21760?

Greatest common factor (GCF) of 21750 and 21760 is 10.

GCF(21750,21760) = 10

We will now calculate the prime factors of 21750 and 21760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21750 and 21760.

How to find the GCF of 21750 and 21760?

We will first find the prime factorization of 21750 and 21760. After we will calculate the factors of 21750 and 21760 and find the biggest common factor number .

Step-1: Prime Factorization of 21750

Prime factors of 21750 are 2, 3, 5, 29. Prime factorization of 21750 in exponential form is:

21750 = 2¹ × 3¹ × 5³ × 29¹

Step-2: Prime Factorization of 21760

Prime factors of 21760 are 2, 5, 17. Prime factorization of 21760 in exponential form is:

21760 = 2⁸ × 5¹ × 17¹

Step-3: Factors of 21750

List of positive integer factors of 21750 that divides 21750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 29, 30, 50, 58, 75, 87, 125, 145, 150, 174, 250, 290, 375, 435, 725, 750, 870, 1450, 2175, 3625, 4350, 7250, 10875

Step-4: Factors of 21760

List of positive integer factors of 21760 that divides 21750 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 64, 68, 80, 85, 128, 136, 160, 170, 256, 272, 320, 340, 544, 640, 680, 1088, 1280, 1360, 2176, 2720, 4352, 5440, 10880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21750 and 21760. The biggest common factor number is the GCF number.
So the greatest common factor 21750 and 21760 is 10.

Also check out the Least Common Multiple of 21750 and 21760