What is the Greatest Common Factor of 69648 and 69664?

Greatest common factor (GCF) of 69648 and 69664 is 16.

GCF(69648,69664) = 16

We will now calculate the prime factors of 69648 and 69664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69648 and 69664.

How to find the GCF of 69648 and 69664?

We will first find the prime factorization of 69648 and 69664. After we will calculate the factors of 69648 and 69664 and find the biggest common factor number .

Step-1: Prime Factorization of 69648

Prime factors of 69648 are 2, 3, 1451. Prime factorization of 69648 in exponential form is:

69648 = 2⁴ × 3¹ × 1451¹

Step-2: 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-3: Factors of 69648

List of positive integer factors of 69648 that divides 69648 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1451, 2902, 4353, 5804, 8706, 11608, 17412, 23216, 34824

Step-4: Factors of 69664

List of positive integer factors of 69664 that divides 69648 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69648 and 69664. The biggest common factor number is the GCF number.
So the greatest common factor 69648 and 69664 is 16.

Also check out the Least Common Multiple of 69648 and 69664