What is the Greatest Common Factor of 71972 and 71984?

Greatest common factor (GCF) of 71972 and 71984 is 4.

GCF(71972,71984) = 4

We will now calculate the prime factors of 71972 and 71984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71972 and 71984.

How to find the GCF of 71972 and 71984?

We will first find the prime factorization of 71972 and 71984. After we will calculate the factors of 71972 and 71984 and find the biggest common factor number .

Step-1: Prime Factorization of 71972

Prime factors of 71972 are 2, 19, 947. Prime factorization of 71972 in exponential form is:

71972 = 2² × 19¹ × 947¹

Step-2: 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-3: Factors of 71972

List of positive integer factors of 71972 that divides 71972 without a remainder.

1, 2, 4, 19, 38, 76, 947, 1894, 3788, 17993, 35986

Step-4: Factors of 71984

List of positive integer factors of 71984 that divides 71972 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71972 and 71984. The biggest common factor number is the GCF number.
So the greatest common factor 71972 and 71984 is 4.

Also check out the Least Common Multiple of 71972 and 71984