What is the Greatest Common Factor of 83974 and 83984?

Greatest common factor (GCF) of 83974 and 83984 is 2.

GCF(83974,83984) = 2

We will now calculate the prime factors of 83974 and 83984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83974 and 83984.

How to find the GCF of 83974 and 83984?

We will first find the prime factorization of 83974 and 83984. After we will calculate the factors of 83974 and 83984 and find the biggest common factor number .

Step-1: Prime Factorization of 83974

Prime factors of 83974 are 2, 11, 347. Prime factorization of 83974 in exponential form is:

83974 = 2¹ × 11² × 347¹

Step-2: Prime Factorization of 83984

Prime factors of 83984 are 2, 29, 181. Prime factorization of 83984 in exponential form is:

83984 = 2⁴ × 29¹ × 181¹

Step-3: Factors of 83974

List of positive integer factors of 83974 that divides 83974 without a remainder.

1, 2, 11, 22, 121, 242, 347, 694, 3817, 7634, 41987

Step-4: Factors of 83984

List of positive integer factors of 83984 that divides 83974 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 181, 232, 362, 464, 724, 1448, 2896, 5249, 10498, 20996, 41992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83974 and 83984. The biggest common factor number is the GCF number.
So the greatest common factor 83974 and 83984 is 2.

Also check out the Least Common Multiple of 83974 and 83984