What is the Greatest Common Factor of 30464 and 30480?

Greatest common factor (GCF) of 30464 and 30480 is 16.

GCF(30464,30480) = 16

We will now calculate the prime factors of 30464 and 30480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30464 and 30480.

How to find the GCF of 30464 and 30480?

We will first find the prime factorization of 30464 and 30480. After we will calculate the factors of 30464 and 30480 and find the biggest common factor number .

Step-1: Prime Factorization of 30464

Prime factors of 30464 are 2, 7, 17. Prime factorization of 30464 in exponential form is:

30464 = 2⁸ × 7¹ × 17¹

Step-2: Prime Factorization of 30480

Prime factors of 30480 are 2, 3, 5, 127. Prime factorization of 30480 in exponential form is:

30480 = 2⁴ × 3¹ × 5¹ × 127¹

Step-3: Factors of 30464

List of positive integer factors of 30464 that divides 30464 without a remainder.

1, 2, 4, 7, 8, 14, 16, 17, 28, 32, 34, 56, 64, 68, 112, 119, 128, 136, 224, 238, 256, 272, 448, 476, 544, 896, 952, 1088, 1792, 1904, 2176, 3808, 4352, 7616, 15232

Step-4: Factors of 30480

List of positive integer factors of 30480 that divides 30464 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 127, 240, 254, 381, 508, 635, 762, 1016, 1270, 1524, 1905, 2032, 2540, 3048, 3810, 5080, 6096, 7620, 10160, 15240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30464 and 30480. The biggest common factor number is the GCF number.
So the greatest common factor 30464 and 30480 is 16.

Also check out the Least Common Multiple of 30464 and 30480