What is the Greatest Common Factor of 69664 and 69680?

Greatest common factor (GCF) of 69664 and 69680 is 16.

GCF(69664,69680) = 16

We will now calculate the prime factors of 69664 and 69680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69664 and 69680.

How to find the GCF of 69664 and 69680?

We will first find the prime factorization of 69664 and 69680. After we will calculate the factors of 69664 and 69680 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 69680

Prime factors of 69680 are 2, 5, 13, 67. Prime factorization of 69680 in exponential form is:

69680 = 2⁴ × 5¹ × 13¹ × 67¹

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 69680

List of positive integer factors of 69680 that divides 69664 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 40, 52, 65, 67, 80, 104, 130, 134, 208, 260, 268, 335, 520, 536, 670, 871, 1040, 1072, 1340, 1742, 2680, 3484, 4355, 5360, 6968, 8710, 13936, 17420, 34840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69664 and 69680. The biggest common factor number is the GCF number.
So the greatest common factor 69664 and 69680 is 16.

Also check out the Least Common Multiple of 69664 and 69680