What is the Greatest Common Factor of 65688 and 65700?

Greatest common factor (GCF) of 65688 and 65700 is 12.

GCF(65688,65700) = 12

We will now calculate the prime factors of 65688 and 65700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65688 and 65700.

How to find the GCF of 65688 and 65700?

We will first find the prime factorization of 65688 and 65700. After we will calculate the factors of 65688 and 65700 and find the biggest common factor number .

Step-1: Prime Factorization of 65688

Prime factors of 65688 are 2, 3, 7, 17, 23. Prime factorization of 65688 in exponential form is:

65688 = 2³ × 3¹ × 7¹ × 17¹ × 23¹

Step-2: Prime Factorization of 65700

Prime factors of 65700 are 2, 3, 5, 73. Prime factorization of 65700 in exponential form is:

65700 = 2² × 3² × 5² × 73¹

Step-3: Factors of 65688

List of positive integer factors of 65688 that divides 65688 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 23, 24, 28, 34, 42, 46, 51, 56, 68, 69, 84, 92, 102, 119, 136, 138, 161, 168, 184, 204, 238, 276, 322, 357, 391, 408, 476, 483, 552, 644, 714, 782, 952, 966, 1173, 1288, 1428, 1564, 1932, 2346, 2737, 2856, 3128, 3864, 4692, 5474, 8211, 9384, 10948, 16422, 21896, 32844

Step-4: Factors of 65700

List of positive integer factors of 65700 that divides 65688 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 73, 75, 90, 100, 146, 150, 180, 219, 225, 292, 300, 365, 438, 450, 657, 730, 876, 900, 1095, 1314, 1460, 1825, 2190, 2628, 3285, 3650, 4380, 5475, 6570, 7300, 10950, 13140, 16425, 21900, 32850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65688 and 65700. The biggest common factor number is the GCF number.
So the greatest common factor 65688 and 65700 is 12.

Also check out the Least Common Multiple of 65688 and 65700