What is the Greatest Common Factor of 70209 and 70224?

Greatest common factor (GCF) of 70209 and 70224 is 3.

GCF(70209,70224) = 3

We will now calculate the prime factors of 70209 and 70224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70209 and 70224.

How to find the GCF of 70209 and 70224?

We will first find the prime factorization of 70209 and 70224. After we will calculate the factors of 70209 and 70224 and find the biggest common factor number .

Step-1: Prime Factorization of 70209

Prime factors of 70209 are 3, 29, 269. Prime factorization of 70209 in exponential form is:

70209 = 3² × 29¹ × 269¹

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 70209

List of positive integer factors of 70209 that divides 70209 without a remainder.

1, 3, 9, 29, 87, 261, 269, 807, 2421, 7801, 23403

Step-4: Factors of 70224

List of positive integer factors of 70224 that divides 70209 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 70209 and 70224. The biggest common factor number is the GCF number.
So the greatest common factor 70209 and 70224 is 3.

Also check out the Least Common Multiple of 70209 and 70224