What is the Greatest Common Factor of 71649 and 71664?

Greatest common factor (GCF) of 71649 and 71664 is 3.

GCF(71649,71664) = 3

We will now calculate the prime factors of 71649 and 71664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71649 and 71664.

How to find the GCF of 71649 and 71664?

We will first find the prime factorization of 71649 and 71664. After we will calculate the factors of 71649 and 71664 and find the biggest common factor number .

Step-1: Prime Factorization of 71649

Prime factors of 71649 are 3, 19, 419. Prime factorization of 71649 in exponential form is:

71649 = 3² × 19¹ × 419¹

Step-2: 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-3: Factors of 71649

List of positive integer factors of 71649 that divides 71649 without a remainder.

1, 3, 9, 19, 57, 171, 419, 1257, 3771, 7961, 23883

Step-4: Factors of 71664

List of positive integer factors of 71664 that divides 71649 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71649 and 71664. The biggest common factor number is the GCF number.
So the greatest common factor 71649 and 71664 is 3.

Also check out the Least Common Multiple of 71649 and 71664