What is the Greatest Common Factor of 71664 and 71684?

Greatest common factor (GCF) of 71664 and 71684 is 4.

GCF(71664,71684) = 4

We will now calculate the prime factors of 71664 and 71684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71664 and 71684.

How to find the GCF of 71664 and 71684?

We will first find the prime factorization of 71664 and 71684. After we will calculate the factors of 71664 and 71684 and find the biggest common factor number .

Step-1: Prime Factorization of 71664

Prime factors of 71664 are 2, 3, 1493. Prime factorization of 71664 in exponential form is:

71664 = 2⁴ × 3¹ × 1493¹

Step-2: Prime Factorization of 71684

Prime factors of 71684 are 2, 17921. Prime factorization of 71684 in exponential form is:

71684 = 2² × 17921¹

Step-3: Factors of 71664

List of positive integer factors of 71664 that divides 71664 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1493, 2986, 4479, 5972, 8958, 11944, 17916, 23888, 35832

Step-4: Factors of 71684

List of positive integer factors of 71684 that divides 71664 without a remainder.

1, 2, 4, 17921, 35842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71664 and 71684. The biggest common factor number is the GCF number.
So the greatest common factor 71664 and 71684 is 4.

Also check out the Least Common Multiple of 71664 and 71684