What is the Greatest Common Factor of 30828 and 30840?

Greatest common factor (GCF) of 30828 and 30840 is 12.

GCF(30828,30840) = 12

We will now calculate the prime factors of 30828 and 30840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30828 and 30840.

How to find the GCF of 30828 and 30840?

We will first find the prime factorization of 30828 and 30840. After we will calculate the factors of 30828 and 30840 and find the biggest common factor number .

Step-1: Prime Factorization of 30828

Prime factors of 30828 are 2, 3, 7, 367. Prime factorization of 30828 in exponential form is:

30828 = 2² × 3¹ × 7¹ × 367¹

Step-2: Prime Factorization of 30840

Prime factors of 30840 are 2, 3, 5, 257. Prime factorization of 30840 in exponential form is:

30840 = 2³ × 3¹ × 5¹ × 257¹

Step-3: Factors of 30828

List of positive integer factors of 30828 that divides 30828 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, 367, 734, 1101, 1468, 2202, 2569, 4404, 5138, 7707, 10276, 15414

Step-4: Factors of 30840

List of positive integer factors of 30840 that divides 30828 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 257, 514, 771, 1028, 1285, 1542, 2056, 2570, 3084, 3855, 5140, 6168, 7710, 10280, 15420

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30828 and 30840. The biggest common factor number is the GCF number.
So the greatest common factor 30828 and 30840 is 12.

Also check out the Least Common Multiple of 30828 and 30840