What is the Greatest Common Factor of 19740 and 19749?

Greatest common factor (GCF) of 19740 and 19749 is 3.

GCF(19740,19749) = 3

We will now calculate the prime factors of 19740 and 19749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19740 and 19749.

How to find the GCF of 19740 and 19749?

We will first find the prime factorization of 19740 and 19749. After we will calculate the factors of 19740 and 19749 and find the biggest common factor number .

Step-1: Prime Factorization of 19740

Prime factors of 19740 are 2, 3, 5, 7, 47. Prime factorization of 19740 in exponential form is:

19740 = 2² × 3¹ × 5¹ × 7¹ × 47¹

Step-2: 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-3: Factors of 19740

List of positive integer factors of 19740 that divides 19740 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 47, 60, 70, 84, 94, 105, 140, 141, 188, 210, 235, 282, 329, 420, 470, 564, 658, 705, 940, 987, 1316, 1410, 1645, 1974, 2820, 3290, 3948, 4935, 6580, 9870

Step-4: Factors of 19749

List of positive integer factors of 19749 that divides 19740 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19740 and 19749. The biggest common factor number is the GCF number.
So the greatest common factor 19740 and 19749 is 3.

Also check out the Least Common Multiple of 19740 and 19749