What is the Greatest Common Factor of 19684 and 19702?

Greatest common factor (GCF) of 19684 and 19702 is 2.

GCF(19684,19702) = 2

We will now calculate the prime factors of 19684 and 19702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19684 and 19702.

How to find the GCF of 19684 and 19702?

We will first find the prime factorization of 19684 and 19702. After we will calculate the factors of 19684 and 19702 and find the biggest common factor number .

Step-1: Prime Factorization of 19684

Prime factors of 19684 are 2, 7, 19, 37. Prime factorization of 19684 in exponential form is:

19684 = 2² × 7¹ × 19¹ × 37¹

Step-2: Prime Factorization of 19702

Prime factors of 19702 are 2, 9851. Prime factorization of 19702 in exponential form is:

19702 = 2¹ × 9851¹

Step-3: Factors of 19684

List of positive integer factors of 19684 that divides 19684 without a remainder.

1, 2, 4, 7, 14, 19, 28, 37, 38, 74, 76, 133, 148, 259, 266, 518, 532, 703, 1036, 1406, 2812, 4921, 9842

Step-4: Factors of 19702

List of positive integer factors of 19702 that divides 19684 without a remainder.

1, 2, 9851

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19684 and 19702. The biggest common factor number is the GCF number.
So the greatest common factor 19684 and 19702 is 2.

Also check out the Least Common Multiple of 19684 and 19702