What is the Greatest Common Factor of 70208 and 70224?

Greatest common factor (GCF) of 70208 and 70224 is 16.

GCF(70208,70224) = 16

We will now calculate the prime factors of 70208 and 70224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70208 and 70224.

How to find the GCF of 70208 and 70224?

We will first find the prime factorization of 70208 and 70224. After we will calculate the factors of 70208 and 70224 and find the biggest common factor number .

Step-1: Prime Factorization of 70208

Prime factors of 70208 are 2, 1097. Prime factorization of 70208 in exponential form is:

70208 = 2⁶ × 1097¹

Step-2: Prime Factorization of 70224

Prime factors of 70224 are 2, 3, 7, 11, 19. Prime factorization of 70224 in exponential form is:

70224 = 2⁴ × 3¹ × 7¹ × 11¹ × 19¹

Step-3: Factors of 70208

List of positive integer factors of 70208 that divides 70208 without a remainder.

1, 2, 4, 8, 16, 32, 64, 1097, 2194, 4388, 8776, 17552, 35104

Step-4: Factors of 70224

List of positive integer factors of 70224 that divides 70208 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 19, 21, 22, 24, 28, 33, 38, 42, 44, 48, 56, 57, 66, 76, 77, 84, 88, 112, 114, 132, 133, 152, 154, 168, 176, 209, 228, 231, 264, 266, 304, 308, 336, 399, 418, 456, 462, 528, 532, 616, 627, 798, 836, 912, 924, 1064, 1232, 1254, 1463, 1596, 1672, 1848, 2128, 2508, 2926, 3192, 3344, 3696, 4389, 5016, 5852, 6384, 8778, 10032, 11704, 17556, 23408, 35112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 70208 and 70224. The biggest common factor number is the GCF number.
So the greatest common factor 70208 and 70224 is 16.

Also check out the Least Common Multiple of 70208 and 70224