What is the Greatest Common Factor of 39504 and 39520?

Greatest common factor (GCF) of 39504 and 39520 is 16.

GCF(39504,39520) = 16

We will now calculate the prime factors of 39504 and 39520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39504 and 39520.

How to find the GCF of 39504 and 39520?

We will first find the prime factorization of 39504 and 39520. After we will calculate the factors of 39504 and 39520 and find the biggest common factor number .

Step-1: Prime Factorization of 39504

Prime factors of 39504 are 2, 3, 823. Prime factorization of 39504 in exponential form is:

39504 = 2⁴ × 3¹ × 823¹

Step-2: Prime Factorization of 39520

Prime factors of 39520 are 2, 5, 13, 19. Prime factorization of 39520 in exponential form is:

39520 = 2⁵ × 5¹ × 13¹ × 19¹

Step-3: Factors of 39504

List of positive integer factors of 39504 that divides 39504 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 823, 1646, 2469, 3292, 4938, 6584, 9876, 13168, 19752

Step-4: Factors of 39520

List of positive integer factors of 39520 that divides 39504 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 19, 20, 26, 32, 38, 40, 52, 65, 76, 80, 95, 104, 130, 152, 160, 190, 208, 247, 260, 304, 380, 416, 494, 520, 608, 760, 988, 1040, 1235, 1520, 1976, 2080, 2470, 3040, 3952, 4940, 7904, 9880, 19760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39504 and 39520. The biggest common factor number is the GCF number.
So the greatest common factor 39504 and 39520 is 16.

Also check out the Least Common Multiple of 39504 and 39520