What is the Greatest Common Factor of 19642 and 19648?

Greatest common factor (GCF) of 19642 and 19648 is 2.

GCF(19642,19648) = 2

We will now calculate the prime factors of 19642 and 19648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19642 and 19648.

How to find the GCF of 19642 and 19648?

We will first find the prime factorization of 19642 and 19648. After we will calculate the factors of 19642 and 19648 and find the biggest common factor number .

Step-1: Prime Factorization of 19642

Prime factors of 19642 are 2, 7, 23, 61. Prime factorization of 19642 in exponential form is:

19642 = 2¹ × 7¹ × 23¹ × 61¹

Step-2: Prime Factorization of 19648

Prime factors of 19648 are 2, 307. Prime factorization of 19648 in exponential form is:

19648 = 2⁶ × 307¹

Step-3: Factors of 19642

List of positive integer factors of 19642 that divides 19642 without a remainder.

1, 2, 7, 14, 23, 46, 61, 122, 161, 322, 427, 854, 1403, 2806, 9821

Step-4: Factors of 19648

List of positive integer factors of 19648 that divides 19642 without a remainder.

1, 2, 4, 8, 16, 32, 64, 307, 614, 1228, 2456, 4912, 9824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19642 and 19648. The biggest common factor number is the GCF number.
So the greatest common factor 19642 and 19648 is 2.

Also check out the Least Common Multiple of 19642 and 19648