What is the Greatest Common Factor of 19749 and 19765?

Greatest common factor (GCF) of 19749 and 19765 is 1.

GCF(19749,19765) = 1

We will now calculate the prime factors of 19749 and 19765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19749 and 19765.

How to find the GCF of 19749 and 19765?

We will first find the prime factorization of 19749 and 19765. After we will calculate the factors of 19749 and 19765 and find the biggest common factor number .

Step-1: Prime Factorization of 19749

Prime factors of 19749 are 3, 29, 227. Prime factorization of 19749 in exponential form is:

19749 = 3¹ × 29¹ × 227¹

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 19749

List of positive integer factors of 19749 that divides 19749 without a remainder.

1, 3, 29, 87, 227, 681, 6583

Step-4: Factors of 19765

List of positive integer factors of 19765 that divides 19749 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19749 and 19765. The biggest common factor number is the GCF number.
So the greatest common factor 19749 and 19765 is 1.

Also check out the Least Common Multiple of 19749 and 19765