What is the Greatest Common Factor of 65688 and 65705?

Greatest common factor (GCF) of 65688 and 65705 is 17.

GCF(65688,65705) = 17

We will now calculate the prime factors of 65688 and 65705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65688 and 65705.

How to find the GCF of 65688 and 65705?

We will first find the prime factorization of 65688 and 65705. After we will calculate the factors of 65688 and 65705 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 65705

Prime factors of 65705 are 5, 17, 773. Prime factorization of 65705 in exponential form is:

65705 = 5¹ × 17¹ × 773¹

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 65705

List of positive integer factors of 65705 that divides 65688 without a remainder.

1, 5, 17, 85, 773, 3865, 13141

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65688 and 65705. The biggest common factor number is the GCF number.
So the greatest common factor 65688 and 65705 is 17.

Also check out the Least Common Multiple of 65688 and 65705