What is the Greatest Common Factor of 19760 and 19765?

Greatest common factor (GCF) of 19760 and 19765 is 5.

GCF(19760,19765) = 5

We will now calculate the prime factors of 19760 and 19765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19760 and 19765.

How to find the GCF of 19760 and 19765?

We will first find the prime factorization of 19760 and 19765. After we will calculate the factors of 19760 and 19765 and find the biggest common factor number .

Step-1: Prime Factorization of 19760

Prime factors of 19760 are 2, 5, 13, 19. Prime factorization of 19760 in exponential form is:

19760 = 2⁴ × 5¹ × 13¹ × 19¹

Step-2: Prime Factorization of 19765

Prime factors of 19765 are 5, 59, 67. Prime factorization of 19765 in exponential form is:

19765 = 5¹ × 59¹ × 67¹

Step-3: Factors of 19760

List of positive integer factors of 19760 that divides 19760 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 19, 20, 26, 38, 40, 52, 65, 76, 80, 95, 104, 130, 152, 190, 208, 247, 260, 304, 380, 494, 520, 760, 988, 1040, 1235, 1520, 1976, 2470, 3952, 4940, 9880

Step-4: Factors of 19765

List of positive integer factors of 19765 that divides 19760 without a remainder.

1, 5, 59, 67, 295, 335, 3953

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19760 and 19765. The biggest common factor number is the GCF number.
So the greatest common factor 19760 and 19765 is 5.

Also check out the Least Common Multiple of 19760 and 19765