What is the Greatest Common Factor of 19667 and 19684?

Greatest common factor (GCF) of 19667 and 19684 is 1.

GCF(19667,19684) = 1

We will now calculate the prime factors of 19667 and 19684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19667 and 19684.

How to find the GCF of 19667 and 19684?

We will first find the prime factorization of 19667 and 19684. After we will calculate the factors of 19667 and 19684 and find the biggest common factor number .

Step-1: Prime Factorization of 19667

Prime factors of 19667 are 71, 277. Prime factorization of 19667 in exponential form is:

19667 = 71¹ × 277¹

Step-2: 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-3: Factors of 19667

List of positive integer factors of 19667 that divides 19667 without a remainder.

1, 71, 277

Step-4: Factors of 19684

List of positive integer factors of 19684 that divides 19667 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19667 and 19684. The biggest common factor number is the GCF number.
So the greatest common factor 19667 and 19684 is 1.

Also check out the Least Common Multiple of 19667 and 19684