What is the Greatest Common Factor of 70304 and 70320?

Greatest common factor (GCF) of 70304 and 70320 is 16.

GCF(70304,70320) = 16

We will now calculate the prime factors of 70304 and 70320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70304 and 70320.

How to find the GCF of 70304 and 70320?

We will first find the prime factorization of 70304 and 70320. After we will calculate the factors of 70304 and 70320 and find the biggest common factor number .

Step-1: Prime Factorization of 70304

Prime factors of 70304 are 2, 13. Prime factorization of 70304 in exponential form is:

70304 = 2⁵ × 13³

Step-2: Prime Factorization of 70320

Prime factors of 70320 are 2, 3, 5, 293. Prime factorization of 70320 in exponential form is:

70320 = 2⁴ × 3¹ × 5¹ × 293¹

Step-3: Factors of 70304

List of positive integer factors of 70304 that divides 70304 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 169, 208, 338, 416, 676, 1352, 2197, 2704, 4394, 5408, 8788, 17576, 35152

Step-4: Factors of 70320

List of positive integer factors of 70320 that divides 70304 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 293, 586, 879, 1172, 1465, 1758, 2344, 2930, 3516, 4395, 4688, 5860, 7032, 8790, 11720, 14064, 17580, 23440, 35160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70304 and 70320. The biggest common factor number is the GCF number.
So the greatest common factor 70304 and 70320 is 16.

Also check out the Least Common Multiple of 70304 and 70320