What is the Greatest Common Factor of 30825 and 30840?

Greatest common factor (GCF) of 30825 and 30840 is 15.

GCF(30825,30840) = 15

We will now calculate the prime factors of 30825 and 30840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30825 and 30840.

How to find the GCF of 30825 and 30840?

We will first find the prime factorization of 30825 and 30840. After we will calculate the factors of 30825 and 30840 and find the biggest common factor number .

Step-1: Prime Factorization of 30825

Prime factors of 30825 are 3, 5, 137. Prime factorization of 30825 in exponential form is:

30825 = 3² × 5² × 137¹

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 30825

List of positive integer factors of 30825 that divides 30825 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 137, 225, 411, 685, 1233, 2055, 3425, 6165, 10275

Step-4: Factors of 30840

List of positive integer factors of 30840 that divides 30825 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 30825 and 30840. The biggest common factor number is the GCF number.
So the greatest common factor 30825 and 30840 is 15.

Also check out the Least Common Multiple of 30825 and 30840