What is the Greatest Common Factor of 19969 and 19988?

Greatest common factor (GCF) of 19969 and 19988 is 19.

GCF(19969,19988) = 19

We will now calculate the prime factors of 19969 and 19988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19969 and 19988.

How to find the GCF of 19969 and 19988?

We will first find the prime factorization of 19969 and 19988. After we will calculate the factors of 19969 and 19988 and find the biggest common factor number .

Step-1: Prime Factorization of 19969

Prime factors of 19969 are 19, 1051. Prime factorization of 19969 in exponential form is:

19969 = 19¹ × 1051¹

Step-2: Prime Factorization of 19988

Prime factors of 19988 are 2, 19, 263. Prime factorization of 19988 in exponential form is:

19988 = 2² × 19¹ × 263¹

Step-3: Factors of 19969

List of positive integer factors of 19969 that divides 19969 without a remainder.

1, 19, 1051

Step-4: Factors of 19988

List of positive integer factors of 19988 that divides 19969 without a remainder.

1, 2, 4, 19, 38, 76, 263, 526, 1052, 4997, 9994

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19969 and 19988. The biggest common factor number is the GCF number.
So the greatest common factor 19969 and 19988 is 19.

Also check out the Least Common Multiple of 19969 and 19988