What is the Greatest Common Factor of 39704 and 39712?

Greatest common factor (GCF) of 39704 and 39712 is 8.

GCF(39704,39712) = 8

We will now calculate the prime factors of 39704 and 39712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39704 and 39712.

How to find the GCF of 39704 and 39712?

We will first find the prime factorization of 39704 and 39712. After we will calculate the factors of 39704 and 39712 and find the biggest common factor number .

Step-1: Prime Factorization of 39704

Prime factors of 39704 are 2, 7, 709. Prime factorization of 39704 in exponential form is:

39704 = 2³ × 7¹ × 709¹

Step-2: Prime Factorization of 39712

Prime factors of 39712 are 2, 17, 73. Prime factorization of 39712 in exponential form is:

39712 = 2⁵ × 17¹ × 73¹

Step-3: Factors of 39704

List of positive integer factors of 39704 that divides 39704 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 709, 1418, 2836, 4963, 5672, 9926, 19852

Step-4: Factors of 39712

List of positive integer factors of 39712 that divides 39704 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 73, 136, 146, 272, 292, 544, 584, 1168, 1241, 2336, 2482, 4964, 9928, 19856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39704 and 39712. The biggest common factor number is the GCF number.
So the greatest common factor 39704 and 39712 is 8.

Also check out the Least Common Multiple of 39704 and 39712