What is the Greatest Common Factor of 65674 and 65688?

Greatest common factor (GCF) of 65674 and 65688 is 14.

GCF(65674,65688) = 14

We will now calculate the prime factors of 65674 and 65688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65674 and 65688.

How to find the GCF of 65674 and 65688?

We will first find the prime factorization of 65674 and 65688. After we will calculate the factors of 65674 and 65688 and find the biggest common factor number .

Step-1: Prime Factorization of 65674

Prime factors of 65674 are 2, 7, 4691. Prime factorization of 65674 in exponential form is:

65674 = 2¹ × 7¹ × 4691¹

Step-2: 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-3: Factors of 65674

List of positive integer factors of 65674 that divides 65674 without a remainder.

1, 2, 7, 14, 4691, 9382, 32837

Step-4: Factors of 65688

List of positive integer factors of 65688 that divides 65674 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65674 and 65688. The biggest common factor number is the GCF number.
So the greatest common factor 65674 and 65688 is 14.

Also check out the Least Common Multiple of 65674 and 65688