What is the Greatest Common Factor of 19712 and 19730?

Greatest common factor (GCF) of 19712 and 19730 is 2.

GCF(19712,19730) = 2

We will now calculate the prime factors of 19712 and 19730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19712 and 19730.

How to find the GCF of 19712 and 19730?

We will first find the prime factorization of 19712 and 19730. After we will calculate the factors of 19712 and 19730 and find the biggest common factor number .

Step-1: Prime Factorization of 19712

Prime factors of 19712 are 2, 7, 11. Prime factorization of 19712 in exponential form is:

19712 = 2⁸ × 7¹ × 11¹

Step-2: 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-3: Factors of 19712

List of positive integer factors of 19712 that divides 19712 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 56, 64, 77, 88, 112, 128, 154, 176, 224, 256, 308, 352, 448, 616, 704, 896, 1232, 1408, 1792, 2464, 2816, 4928, 9856

Step-4: Factors of 19730

List of positive integer factors of 19730 that divides 19712 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19712 and 19730. The biggest common factor number is the GCF number.
So the greatest common factor 19712 and 19730 is 2.

Also check out the Least Common Multiple of 19712 and 19730