What is the Greatest Common Factor of 19978 and 19992?

Greatest common factor (GCF) of 19978 and 19992 is 14.

GCF(19978,19992) = 14

We will now calculate the prime factors of 19978 and 19992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19978 and 19992.

How to find the GCF of 19978 and 19992?

We will first find the prime factorization of 19978 and 19992. After we will calculate the factors of 19978 and 19992 and find the biggest common factor number .

Step-1: Prime Factorization of 19978

Prime factors of 19978 are 2, 7, 1427. Prime factorization of 19978 in exponential form is:

19978 = 2¹ × 7¹ × 1427¹

Step-2: Prime Factorization of 19992

Prime factors of 19992 are 2, 3, 7, 17. Prime factorization of 19992 in exponential form is:

19992 = 2³ × 3¹ × 7² × 17¹

Step-3: Factors of 19978

List of positive integer factors of 19978 that divides 19978 without a remainder.

1, 2, 7, 14, 1427, 2854, 9989

Step-4: Factors of 19992

List of positive integer factors of 19992 that divides 19978 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 49, 51, 56, 68, 84, 98, 102, 119, 136, 147, 168, 196, 204, 238, 294, 357, 392, 408, 476, 588, 714, 833, 952, 1176, 1428, 1666, 2499, 2856, 3332, 4998, 6664, 9996

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19978 and 19992. The biggest common factor number is the GCF number.
So the greatest common factor 19978 and 19992 is 14.

Also check out the Least Common Multiple of 19978 and 19992