What is the Greatest Common Factor of 19740 and 19755?

Greatest common factor (GCF) of 19740 and 19755 is 15.

GCF(19740,19755) = 15

We will now calculate the prime factors of 19740 and 19755, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19740 and 19755.

How to find the GCF of 19740 and 19755?

We will first find the prime factorization of 19740 and 19755. After we will calculate the factors of 19740 and 19755 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 19755

Prime factors of 19755 are 3, 5, 439. Prime factorization of 19755 in exponential form is:

19755 = 3² × 5¹ × 439¹

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 19755

List of positive integer factors of 19755 that divides 19740 without a remainder.

1, 3, 5, 9, 15, 45, 439, 1317, 2195, 3951, 6585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19740 and 19755. The biggest common factor number is the GCF number.
So the greatest common factor 19740 and 19755 is 15.

Also check out the Least Common Multiple of 19740 and 19755