What is the Greatest Common Factor of 19749 and 19758?

Greatest common factor (GCF) of 19749 and 19758 is 3.

GCF(19749,19758) = 3

We will now calculate the prime factors of 19749 and 19758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19749 and 19758.

How to find the GCF of 19749 and 19758?

We will first find the prime factorization of 19749 and 19758. After we will calculate the factors of 19749 and 19758 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 19758

Prime factors of 19758 are 2, 3, 37, 89. Prime factorization of 19758 in exponential form is:

19758 = 2¹ × 3¹ × 37¹ × 89¹

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 19758

List of positive integer factors of 19758 that divides 19749 without a remainder.

1, 2, 3, 6, 37, 74, 89, 111, 178, 222, 267, 534, 3293, 6586, 9879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19749 and 19758. The biggest common factor number is the GCF number.
So the greatest common factor 19749 and 19758 is 3.

Also check out the Least Common Multiple of 19749 and 19758