What is the Greatest Common Factor of 19730 and 19740?

Greatest common factor (GCF) of 19730 and 19740 is 10.

GCF(19730,19740) = 10

We will now calculate the prime factors of 19730 and 19740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19730 and 19740.

How to find the GCF of 19730 and 19740?

We will first find the prime factorization of 19730 and 19740. After we will calculate the factors of 19730 and 19740 and find the biggest common factor number .

Step-1: Prime Factorization of 19730

Prime factors of 19730 are 2, 5, 1973. Prime factorization of 19730 in exponential form is:

19730 = 2¹ × 5¹ × 1973¹

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 19730

List of positive integer factors of 19730 that divides 19730 without a remainder.

1, 2, 5, 10, 1973, 3946, 9865

Step-4: Factors of 19740

List of positive integer factors of 19740 that divides 19730 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 19730 and 19740. The biggest common factor number is the GCF number.
So the greatest common factor 19730 and 19740 is 10.

Also check out the Least Common Multiple of 19730 and 19740