What is the Greatest Common Factor of 19725 and 19740?

Greatest common factor (GCF) of 19725 and 19740 is 15.

GCF(19725,19740) = 15

We will now calculate the prime factors of 19725 and 19740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19725 and 19740.

How to find the GCF of 19725 and 19740?

We will first find the prime factorization of 19725 and 19740. After we will calculate the factors of 19725 and 19740 and find the biggest common factor number .

Step-1: Prime Factorization of 19725

Prime factors of 19725 are 3, 5, 263. Prime factorization of 19725 in exponential form is:

19725 = 3¹ × 5² × 263¹

Step-2: 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-3: Factors of 19725

List of positive integer factors of 19725 that divides 19725 without a remainder.

1, 3, 5, 15, 25, 75, 263, 789, 1315, 3945, 6575

Step-4: Factors of 19740

List of positive integer factors of 19740 that divides 19725 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19725 and 19740. The biggest common factor number is the GCF number.
So the greatest common factor 19725 and 19740 is 15.

Also check out the Least Common Multiple of 19725 and 19740