What is the Greatest Common Factor of 71706 and 71712?

Greatest common factor (GCF) of 71706 and 71712 is 6.

GCF(71706,71712) = 6

We will now calculate the prime factors of 71706 and 71712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71706 and 71712.

How to find the GCF of 71706 and 71712?

We will first find the prime factorization of 71706 and 71712. After we will calculate the factors of 71706 and 71712 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 71712

Prime factors of 71712 are 2, 3, 83. Prime factorization of 71712 in exponential form is:

71712 = 2⁵ × 3³ × 83¹

Step-3: Factors of 71706

List of positive integer factors of 71706 that divides 71706 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

Step-4: Factors of 71712

List of positive integer factors of 71712 that divides 71706 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 83, 96, 108, 144, 166, 216, 249, 288, 332, 432, 498, 664, 747, 864, 996, 1328, 1494, 1992, 2241, 2656, 2988, 3984, 4482, 5976, 7968, 8964, 11952, 17928, 23904, 35856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71706 and 71712. The biggest common factor number is the GCF number.
So the greatest common factor 71706 and 71712 is 6.

Also check out the Least Common Multiple of 71706 and 71712