What is the Greatest Common Factor of 71688 and 71706?

Greatest common factor (GCF) of 71688 and 71706 is 6.

GCF(71688,71706) = 6

We will now calculate the prime factors of 71688 and 71706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71688 and 71706.

How to find the GCF of 71688 and 71706?

We will first find the prime factorization of 71688 and 71706. After we will calculate the factors of 71688 and 71706 and find the biggest common factor number .

Step-1: Prime Factorization of 71688

Prime factors of 71688 are 2, 3, 29, 103. Prime factorization of 71688 in exponential form is:

71688 = 2³ × 3¹ × 29¹ × 103¹

Step-2: Prime Factorization of 71706

Prime factors of 71706 are 2, 3, 17, 19, 37. Prime factorization of 71706 in exponential form is:

71706 = 2¹ × 3¹ × 17¹ × 19¹ × 37¹

Step-3: Factors of 71688

List of positive integer factors of 71688 that divides 71688 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 103, 116, 174, 206, 232, 309, 348, 412, 618, 696, 824, 1236, 2472, 2987, 5974, 8961, 11948, 17922, 23896, 35844

Step-4: Factors of 71706

List of positive integer factors of 71706 that divides 71688 without a remainder.

1, 2, 3, 6, 17, 19, 34, 37, 38, 51, 57, 74, 102, 111, 114, 222, 323, 629, 646, 703, 969, 1258, 1406, 1887, 1938, 2109, 3774, 4218, 11951, 23902, 35853

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71688 and 71706. The biggest common factor number is the GCF number.
So the greatest common factor 71688 and 71706 is 6.

Also check out the Least Common Multiple of 71688 and 71706