What is the Greatest Common Factor of 69664 and 69678?

Greatest common factor (GCF) of 69664 and 69678 is 14.

GCF(69664,69678) = 14

We will now calculate the prime factors of 69664 and 69678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69664 and 69678.

How to find the GCF of 69664 and 69678?

We will first find the prime factorization of 69664 and 69678. After we will calculate the factors of 69664 and 69678 and find the biggest common factor number .

Step-1: Prime Factorization of 69664

Prime factors of 69664 are 2, 7, 311. Prime factorization of 69664 in exponential form is:

69664 = 2⁵ × 7¹ × 311¹

Step-2: Prime Factorization of 69678

Prime factors of 69678 are 2, 3, 7, 79. Prime factorization of 69678 in exponential form is:

69678 = 2¹ × 3² × 7² × 79¹

Step-3: Factors of 69664

List of positive integer factors of 69664 that divides 69664 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 311, 622, 1244, 2177, 2488, 4354, 4976, 8708, 9952, 17416, 34832

Step-4: Factors of 69678

List of positive integer factors of 69678 that divides 69664 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 79, 98, 126, 147, 158, 237, 294, 441, 474, 553, 711, 882, 1106, 1422, 1659, 3318, 3871, 4977, 7742, 9954, 11613, 23226, 34839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69664 and 69678. The biggest common factor number is the GCF number.
So the greatest common factor 69664 and 69678 is 14.

Also check out the Least Common Multiple of 69664 and 69678