What is the Greatest Common Factor of 30450 and 30464?

Greatest common factor (GCF) of 30450 and 30464 is 14.

GCF(30450,30464) = 14

We will now calculate the prime factors of 30450 and 30464, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30450 and 30464.

How to find the GCF of 30450 and 30464?

We will first find the prime factorization of 30450 and 30464. After we will calculate the factors of 30450 and 30464 and find the biggest common factor number .

Step-1: Prime Factorization of 30450

Prime factors of 30450 are 2, 3, 5, 7, 29. Prime factorization of 30450 in exponential form is:

30450 = 2¹ × 3¹ × 5² × 7¹ × 29¹

Step-2: 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-3: Factors of 30450

List of positive integer factors of 30450 that divides 30450 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 29, 30, 35, 42, 50, 58, 70, 75, 87, 105, 145, 150, 174, 175, 203, 210, 290, 350, 406, 435, 525, 609, 725, 870, 1015, 1050, 1218, 1450, 2030, 2175, 3045, 4350, 5075, 6090, 10150, 15225

Step-4: Factors of 30464

List of positive integer factors of 30464 that divides 30450 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30450 and 30464. The biggest common factor number is the GCF number.
So the greatest common factor 30450 and 30464 is 14.

Also check out the Least Common Multiple of 30450 and 30464