What is the Greatest Common Factor of 71984 and 72004?

Greatest common factor (GCF) of 71984 and 72004 is 4.

GCF(71984,72004) = 4

We will now calculate the prime factors of 71984 and 72004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71984 and 72004.

How to find the GCF of 71984 and 72004?

We will first find the prime factorization of 71984 and 72004. After we will calculate the factors of 71984 and 72004 and find the biggest common factor number .

Step-1: Prime Factorization of 71984

Prime factors of 71984 are 2, 11, 409. Prime factorization of 71984 in exponential form is:

71984 = 2⁴ × 11¹ × 409¹

Step-2: Prime Factorization of 72004

Prime factors of 72004 are 2, 47, 383. Prime factorization of 72004 in exponential form is:

72004 = 2² × 47¹ × 383¹

Step-3: Factors of 71984

List of positive integer factors of 71984 that divides 71984 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 409, 818, 1636, 3272, 4499, 6544, 8998, 17996, 35992

Step-4: Factors of 72004

List of positive integer factors of 72004 that divides 71984 without a remainder.

1, 2, 4, 47, 94, 188, 383, 766, 1532, 18001, 36002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71984 and 72004. The biggest common factor number is the GCF number.
So the greatest common factor 71984 and 72004 is 4.

Also check out the Least Common Multiple of 71984 and 72004