What is the Greatest Common Factor of 21760 and 21765?

Greatest common factor (GCF) of 21760 and 21765 is 5.

GCF(21760,21765) = 5

We will now calculate the prime factors of 21760 and 21765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21760 and 21765.

How to find the GCF of 21760 and 21765?

We will first find the prime factorization of 21760 and 21765. After we will calculate the factors of 21760 and 21765 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21765

Prime factors of 21765 are 3, 5, 1451. Prime factorization of 21765 in exponential form is:

21765 = 3¹ × 5¹ × 1451¹

Step-3: Factors of 21760

List of positive integer factors of 21760 that divides 21760 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

Step-4: Factors of 21765

List of positive integer factors of 21765 that divides 21760 without a remainder.

1, 3, 5, 15, 1451, 4353, 7255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21760 and 21765. The biggest common factor number is the GCF number.
So the greatest common factor 21760 and 21765 is 5.

Also check out the Least Common Multiple of 21760 and 21765