What is the Greatest Common Factor of 19964 and 19974?

Greatest common factor (GCF) of 19964 and 19974 is 2.

GCF(19964,19974) = 2

We will now calculate the prime factors of 19964 and 19974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19964 and 19974.

How to find the GCF of 19964 and 19974?

We will first find the prime factorization of 19964 and 19974. After we will calculate the factors of 19964 and 19974 and find the biggest common factor number .

Step-1: Prime Factorization of 19964

Prime factors of 19964 are 2, 7, 23, 31. Prime factorization of 19964 in exponential form is:

19964 = 2² × 7¹ × 23¹ × 31¹

Step-2: Prime Factorization of 19974

Prime factors of 19974 are 2, 3, 3329. Prime factorization of 19974 in exponential form is:

19974 = 2¹ × 3¹ × 3329¹

Step-3: Factors of 19964

List of positive integer factors of 19964 that divides 19964 without a remainder.

1, 2, 4, 7, 14, 23, 28, 31, 46, 62, 92, 124, 161, 217, 322, 434, 644, 713, 868, 1426, 2852, 4991, 9982

Step-4: Factors of 19974

List of positive integer factors of 19974 that divides 19964 without a remainder.

1, 2, 3, 6, 3329, 6658, 9987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19964 and 19974. The biggest common factor number is the GCF number.
So the greatest common factor 19964 and 19974 is 2.

Also check out the Least Common Multiple of 19964 and 19974